{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Chapter 4 – Training Models**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "_This notebook contains all the sample code and solutions to the exercises in chapter 4._"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "  <td>\n",
    "    <a href=\"https://colab.research.google.com/github/ageron/handson-ml2/blob/master/04_training_linear_models.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>\n",
    "  </td>\n",
    "  <td>\n",
    "    <a target=\"_blank\" href=\"https://kaggle.com/kernels/welcome?src=https://github.com/ageron/handson-ml2/blob/master/04_training_linear_models.ipynb\"><img src=\"https://kaggle.com/static/images/open-in-kaggle.svg\" /></a>\n",
    "  </td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's import a few common modules, ensure MatplotLib plots figures inline and prepare a function to save the figures. We also check that Python 3.5 or later is installed (although Python 2.x may work, it is deprecated so we strongly recommend you use Python 3 instead), as well as Scikit-Learn ≥0.20."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Python ≥3.5 is required\n",
    "import sys\n",
    "assert sys.version_info >= (3, 5)\n",
    "\n",
    "# Scikit-Learn ≥0.20 is required\n",
    "import sklearn\n",
    "assert sklearn.__version__ >= \"0.20\"\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "mpl.rc('axes', labelsize=14)\n",
    "mpl.rc('xtick', labelsize=12)\n",
    "mpl.rc('ytick', labelsize=12)\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"training_linear_models\"\n",
    "IMAGES_PATH = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID)\n",
    "os.makedirs(IMAGES_PATH, exist_ok=True)\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True, fig_extension=\"png\", resolution=300):\n",
    "    path = os.path.join(IMAGES_PATH, fig_id + \".\" + fig_extension)\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format=fig_extension, dpi=resolution)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Normal Equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "X = 2 * np.random.rand(100, 1)\n",
    "y = 4 + 3 * X + np.random.randn(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure generated_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"generated_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_b = np.c_[np.ones((100, 1)), X]  # add x0 = 1 to each instance\n",
    "theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new_b = np.c_[np.ones((2, 1)), X_new]  # add x0 = 1 to each instance\n",
    "y_predict = X_new_b.dot(theta_best)\n",
    "y_predict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.axis([0, 2, 0, 15])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure in the book actually corresponds to the following code, with a legend and axis labels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure linear_model_predictions_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_predict, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 2, 0, 15])\n",
    "save_fig(\"linear_model_predictions_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.21509616]), array([[2.77011339]]))"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg.predict(X_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `LinearRegression` class is based on the `scipy.linalg.lstsq()` function (the name stands for \"least squares\"), which you could call directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_best_svd, residuals, rank, s = np.linalg.lstsq(X_b, y, rcond=1e-6)\n",
    "theta_best_svd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This function computes $\\mathbf{X}^+\\mathbf{y}$, where $\\mathbf{X}^{+}$ is the _pseudoinverse_ of $\\mathbf{X}$ (specifically the Moore-Penrose inverse). You can use `np.linalg.pinv()` to compute the pseudoinverse directly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.pinv(X_b).dot(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gradient Descent\n",
    "## Batch Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.1  # learning rate\n",
    "n_iterations = 1000\n",
    "m = 100\n",
    "\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "    theta = theta - eta * gradients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [2.77011339]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21509616],\n",
       "       [9.75532293]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_new_b.dot(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_bgd = []\n",
    "\n",
    "def plot_gradient_descent(theta, eta, theta_path=None):\n",
    "    m = len(X_b)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    n_iterations = 1000\n",
    "    for iteration in range(n_iterations):\n",
    "        if iteration < 10:\n",
    "            y_predict = X_new_b.dot(theta)\n",
    "            style = \"b-\" if iteration > 0 else \"r--\"\n",
    "            plt.plot(X_new, y_predict, style)\n",
    "        gradients = 2/m * X_b.T.dot(X_b.dot(theta) - y)\n",
    "        theta = theta - eta * gradients\n",
    "        if theta_path is not None:\n",
    "            theta_path.append(theta)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 2, 0, 15])\n",
    "    plt.title(r\"$\\eta = {}$\".format(eta), fontsize=16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.subplot(131); plot_gradient_descent(theta, eta=0.02)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(132); plot_gradient_descent(theta, eta=0.1, theta_path=theta_path_bgd)\n",
    "plt.subplot(133); plot_gradient_descent(theta, eta=0.5)\n",
    "\n",
    "save_fig(\"gradient_descent_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_sgd = []\n",
    "m = len(X_b)\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure sgd_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_epochs = 50\n",
    "t0, t1 = 5, 50  # learning schedule hyperparameters\n",
    "\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "for epoch in range(n_epochs):\n",
    "    for i in range(m):\n",
    "        if epoch == 0 and i < 20:                    # not shown in the book\n",
    "            y_predict = X_new_b.dot(theta)           # not shown\n",
    "            style = \"b-\" if i > 0 else \"r--\"         # not shown\n",
    "            plt.plot(X_new, y_predict, style)        # not shown\n",
    "        random_index = np.random.randint(m)\n",
    "        xi = X_b[random_index:random_index+1]\n",
    "        yi = y[random_index:random_index+1]\n",
    "        gradients = 2 * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(epoch * m + i)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_sgd.append(theta)                 # not shown\n",
    "\n",
    "plt.plot(X, y, \"b.\")                                 # not shown\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)                     # not shown\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)           # not shown\n",
    "plt.axis([0, 2, 0, 15])                              # not shown\n",
    "save_fig(\"sgd_plot\")                                 # not shown\n",
    "plt.show()                                           # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.21076011],\n",
       "       [2.74856079]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDRegressor(eta0=0.1, penalty=None, random_state=42)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDRegressor\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1000, tol=1e-3, penalty=None, eta0=0.1, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.24365286]), array([2.8250878]))"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg.intercept_, sgd_reg.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mini-batch gradient descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_mgd = []\n",
    "\n",
    "n_iterations = 50\n",
    "minibatch_size = 20\n",
    "\n",
    "np.random.seed(42)\n",
    "theta = np.random.randn(2,1)  # random initialization\n",
    "\n",
    "t0, t1 = 200, 1000\n",
    "def learning_schedule(t):\n",
    "    return t0 / (t + t1)\n",
    "\n",
    "t = 0\n",
    "for epoch in range(n_iterations):\n",
    "    shuffled_indices = np.random.permutation(m)\n",
    "    X_b_shuffled = X_b[shuffled_indices]\n",
    "    y_shuffled = y[shuffled_indices]\n",
    "    for i in range(0, m, minibatch_size):\n",
    "        t += 1\n",
    "        xi = X_b_shuffled[i:i+minibatch_size]\n",
    "        yi = y_shuffled[i:i+minibatch_size]\n",
    "        gradients = 2/minibatch_size * xi.T.dot(xi.dot(theta) - yi)\n",
    "        eta = learning_schedule(t)\n",
    "        theta = theta - eta * gradients\n",
    "        theta_path_mgd.append(theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.25214635],\n",
       "       [2.7896408 ]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure gradient_descent_paths_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7,4))\n",
    "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], \"r-s\", linewidth=1, label=\"Stochastic\")\n",
    "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], \"g-+\", linewidth=2, label=\"Mini-batch\")\n",
    "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], \"b-o\", linewidth=3, label=\"Batch\")\n",
    "plt.legend(loc=\"upper left\", fontsize=16)\n",
    "plt.xlabel(r\"$\\theta_0$\", fontsize=20)\n",
    "plt.ylabel(r\"$\\theta_1$   \", fontsize=20, rotation=0)\n",
    "plt.axis([2.5, 4.5, 2.3, 3.9])\n",
    "save_fig(\"gradient_descent_paths_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.random as rnd\n",
    "\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_data_plot\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"quadratic_data_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)\n",
    "X[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.75275929,  0.56664654])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_poly[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.78134581]), array([[0.93366893, 0.56456263]]))"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X_poly, y)\n",
    "lin_reg.intercept_, lin_reg.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure quadratic_predictions_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.transform(X_new)\n",
    "y_new = lin_reg.predict(X_new_poly)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"quadratic_predictions_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure high_degree_polynomials_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n",
    "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    std_scaler = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_regression = Pipeline([\n",
    "            (\"poly_features\", polybig_features),\n",
    "            (\"std_scaler\", std_scaler),\n",
    "            (\"lin_reg\", lin_reg),\n",
    "        ])\n",
    "    polynomial_regression.fit(X, y)\n",
    "    y_newbig = polynomial_regression.predict(X_new)\n",
    "    plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n",
    "\n",
    "plt.plot(X, y, \"b.\", linewidth=3)\n",
    "plt.legend(loc=\"upper left\")\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.axis([-3, 3, 0, 10])\n",
    "save_fig(\"high_degree_polynomials_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning Curves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n",
    "    train_errors, val_errors = [], []\n",
    "    for m in range(1, len(X_train) + 1):\n",
    "        model.fit(X_train[:m], y_train[:m])\n",
    "        y_train_predict = model.predict(X_train[:m])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train[:m], y_train_predict))\n",
    "        val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "    plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"train\")\n",
    "    plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"val\")\n",
    "    plt.legend(loc=\"upper right\", fontsize=14)   # not shown in the book\n",
    "    plt.xlabel(\"Training set size\", fontsize=14) # not shown\n",
    "    plt.ylabel(\"RMSE\", fontsize=14)              # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure underfitting_learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lin_reg = LinearRegression()\n",
    "plot_learning_curves(lin_reg, X, y)\n",
    "plt.axis([0, 80, 0, 3])                         # not shown in the book\n",
    "save_fig(\"underfitting_learning_curves_plot\")   # not shown\n",
    "plt.show()                                      # not shown"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure learning_curves_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "\n",
    "polynomial_regression = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "        (\"lin_reg\", LinearRegression()),\n",
    "    ])\n",
    "\n",
    "plot_learning_curves(polynomial_regression, X, y)\n",
    "plt.axis([0, 80, 0, 3])           # not shown\n",
    "save_fig(\"learning_curves_plot\")  # not shown\n",
    "plt.show()                        # not shown"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularized Linear Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ridge Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.55071465]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "ridge_reg = Ridge(alpha=1, solver=\"cholesky\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.5507201]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridge_reg = Ridge(alpha=1, solver=\"sag\", random_state=42)\n",
    "ridge_reg.fit(X, y)\n",
    "ridge_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure ridge_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "\n",
    "def plot_model(model_class, polynomial, alphas, **model_kargs):\n",
    "    for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n",
    "        model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n",
    "        if polynomial:\n",
    "            model = Pipeline([\n",
    "                    (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n",
    "                    (\"std_scaler\", StandardScaler()),\n",
    "                    (\"regul_reg\", model),\n",
    "                ])\n",
    "        model.fit(X, y)\n",
    "        y_new_regul = model.predict(X_new)\n",
    "        lw = 2 if alpha > 0 else 1\n",
    "        plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\alpha = {}$\".format(alpha))\n",
    "    plt.plot(X, y, \"b.\", linewidth=3)\n",
    "    plt.legend(loc=\"upper left\", fontsize=15)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    plt.axis([0, 3, 0, 4])\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)\n",
    "\n",
    "save_fig(\"ridge_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: to be future-proof, we set `max_iter=1000` and `tol=1e-3` because these will be the default values in Scikit-Learn 0.21."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.47012588])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(penalty=\"l2\", max_iter=1000, tol=1e-3, random_state=42)\n",
    "sgd_reg.fit(X, y.ravel())\n",
    "sgd_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lasso Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ageron/miniconda3/envs/tf2/lib/python3.7/site-packages/sklearn/linear_model/_coordinate_descent.py:531: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Duality gap: 2.802867703827423, tolerance: 0.0009294783355207351\n",
      "  positive)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "\n",
    "plt.figure(figsize=(8,4))\n",
    "plt.subplot(121)\n",
    "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n",
    "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n",
    "plt.subplot(122)\n",
    "plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), random_state=42)\n",
    "\n",
    "save_fig(\"lasso_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.53788174])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "lasso_reg = Lasso(alpha=0.1)\n",
    "lasso_reg.fit(X, y)\n",
    "lasso_reg.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Elastic Net"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.54333232])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import ElasticNet\n",
    "elastic_net = ElasticNet(alpha=0.1, l1_ratio=0.5, random_state=42)\n",
    "elastic_net.fit(X, y)\n",
    "elastic_net.predict([[1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Early Stopping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "m = 100\n",
    "X = 6 * np.random.rand(m, 1) - 3\n",
    "y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n",
    "\n",
    "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from copy import deepcopy\n",
    "\n",
    "poly_scaler = Pipeline([\n",
    "        (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n",
    "        (\"std_scaler\", StandardScaler())\n",
    "    ])\n",
    "\n",
    "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n",
    "X_val_poly_scaled = poly_scaler.transform(X_val)\n",
    "\n",
    "sgd_reg = SGDRegressor(max_iter=1, tol=-np.infty, warm_start=True,\n",
    "                       penalty=None, learning_rate=\"constant\", eta0=0.0005, random_state=42)\n",
    "\n",
    "minimum_val_error = float(\"inf\")\n",
    "best_epoch = None\n",
    "best_model = None\n",
    "for epoch in range(1000):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)  # continues where it left off\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    val_error = mean_squared_error(y_val, y_val_predict)\n",
    "    if val_error < minimum_val_error:\n",
    "        minimum_val_error = val_error\n",
    "        best_epoch = epoch\n",
    "        best_model = deepcopy(sgd_reg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create the graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure early_stopping_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sgd_reg = SGDRegressor(max_iter=1, tol=-np.infty, warm_start=True,\n",
    "                       penalty=None, learning_rate=\"constant\", eta0=0.0005, random_state=42)\n",
    "\n",
    "n_epochs = 500\n",
    "train_errors, val_errors = [], []\n",
    "for epoch in range(n_epochs):\n",
    "    sgd_reg.fit(X_train_poly_scaled, y_train)\n",
    "    y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n",
    "    y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n",
    "    train_errors.append(mean_squared_error(y_train, y_train_predict))\n",
    "    val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "\n",
    "best_epoch = np.argmin(val_errors)\n",
    "best_val_rmse = np.sqrt(val_errors[best_epoch])\n",
    "\n",
    "plt.annotate('Best model',\n",
    "             xy=(best_epoch, best_val_rmse),\n",
    "             xytext=(best_epoch, best_val_rmse + 1),\n",
    "             ha=\"center\",\n",
    "             arrowprops=dict(facecolor='black', shrink=0.05),\n",
    "             fontsize=16,\n",
    "            )\n",
    "\n",
    "best_val_rmse -= 0.03  # just to make the graph look better\n",
    "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n",
    "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n",
    "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n",
    "plt.legend(loc=\"upper right\", fontsize=14)\n",
    "plt.xlabel(\"Epoch\", fontsize=14)\n",
    "plt.ylabel(\"RMSE\", fontsize=14)\n",
    "save_fig(\"early_stopping_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(239,\n",
       " SGDRegressor(eta0=0.0005, learning_rate='constant', max_iter=1, penalty=None,\n",
       "              random_state=42, tol=-inf, warm_start=True))"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best_epoch, best_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "t1a, t1b, t2a, t2b = -1, 3, -1.5, 1.5\n",
    "\n",
    "t1s = np.linspace(t1a, t1b, 500)\n",
    "t2s = np.linspace(t2a, t2b, 500)\n",
    "t1, t2 = np.meshgrid(t1s, t2s)\n",
    "T = np.c_[t1.ravel(), t2.ravel()]\n",
    "Xr = np.array([[1, 1], [1, -1], [1, 0.5]])\n",
    "yr = 2 * Xr[:, :1] + 0.5 * Xr[:, 1:]\n",
    "\n",
    "J = (1/len(Xr) * np.sum((T.dot(Xr.T) - yr.T)**2, axis=1)).reshape(t1.shape)\n",
    "\n",
    "N1 = np.linalg.norm(T, ord=1, axis=1).reshape(t1.shape)\n",
    "N2 = np.linalg.norm(T, ord=2, axis=1).reshape(t1.shape)\n",
    "\n",
    "t_min_idx = np.unravel_index(np.argmin(J), J.shape)\n",
    "t1_min, t2_min = t1[t_min_idx], t2[t_min_idx]\n",
    "\n",
    "t_init = np.array([[0.25], [-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure lasso_vs_ridge_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 727.2x576 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def bgd_path(theta, X, y, l1, l2, core = 1, eta = 0.05, n_iterations = 200):\n",
    "    path = [theta]\n",
    "    for iteration in range(n_iterations):\n",
    "        gradients = core * 2/len(X) * X.T.dot(X.dot(theta) - y) + l1 * np.sign(theta) + l2 * theta\n",
    "        theta = theta - eta * gradients\n",
    "        path.append(theta)\n",
    "    return np.array(path)\n",
    "\n",
    "fig, axes = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10.1, 8))\n",
    "for i, N, l1, l2, title in ((0, N1, 2., 0, \"Lasso\"), (1, N2, 0,  2., \"Ridge\")):\n",
    "    JR = J + l1 * N1 + l2 * 0.5 * N2**2\n",
    "    \n",
    "    tr_min_idx = np.unravel_index(np.argmin(JR), JR.shape)\n",
    "    t1r_min, t2r_min = t1[tr_min_idx], t2[tr_min_idx]\n",
    "\n",
    "    levelsJ=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(J) - np.min(J)) + np.min(J)\n",
    "    levelsJR=(np.exp(np.linspace(0, 1, 20)) - 1) * (np.max(JR) - np.min(JR)) + np.min(JR)\n",
    "    levelsN=np.linspace(0, np.max(N), 10)\n",
    "    \n",
    "    path_J = bgd_path(t_init, Xr, yr, l1=0, l2=0)\n",
    "    path_JR = bgd_path(t_init, Xr, yr, l1, l2)\n",
    "    path_N = bgd_path(np.array([[2.0], [0.5]]), Xr, yr, np.sign(l1)/3, np.sign(l2), core=0)\n",
    "\n",
    "    ax = axes[i, 0]\n",
    "    ax.grid(True)\n",
    "    ax.axhline(y=0, color='k')\n",
    "    ax.axvline(x=0, color='k')\n",
    "    ax.contourf(t1, t2, N / 2., levels=levelsN)\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.set_title(r\"$\\ell_{}$ penalty\".format(i + 1), fontsize=16)\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\", fontsize=16)\n",
    "    ax.set_ylabel(r\"$\\theta_2$\", fontsize=16, rotation=0)\n",
    "\n",
    "    ax = axes[i, 1]\n",
    "    ax.grid(True)\n",
    "    ax.axhline(y=0, color='k')\n",
    "    ax.axvline(x=0, color='k')\n",
    "    ax.contourf(t1, t2, JR, levels=levelsJR, alpha=0.9)\n",
    "    ax.plot(path_JR[:, 0], path_JR[:, 1], \"w-o\")\n",
    "    ax.plot(path_N[:, 0], path_N[:, 1], \"y--\")\n",
    "    ax.plot(0, 0, \"ys\")\n",
    "    ax.plot(t1_min, t2_min, \"ys\")\n",
    "    ax.plot(t1r_min, t2r_min, \"rs\")\n",
    "    ax.set_title(title, fontsize=16)\n",
    "    ax.axis([t1a, t1b, t2a, t2b])\n",
    "    if i == 1:\n",
    "        ax.set_xlabel(r\"$\\theta_1$\", fontsize=16)\n",
    "\n",
    "save_fig(\"lasso_vs_ridge_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Decision Boundaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_function_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(-10, 10, 100)\n",
    "sig = 1 / (1 + np.exp(-t))\n",
    "plt.figure(figsize=(9, 3))\n",
    "plt.plot([-10, 10], [0, 0], \"k-\")\n",
    "plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n",
    "plt.plot([-10, 10], [1, 1], \"k:\")\n",
    "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n",
    "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n",
    "plt.xlabel(\"t\")\n",
    "plt.legend(loc=\"upper left\", fontsize=20)\n",
    "plt.axis([-10, 10, -0.1, 1.1])\n",
    "save_fig(\"logistic_function_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['data',\n",
       " 'target',\n",
       " 'frame',\n",
       " 'target_names',\n",
       " 'DESCR',\n",
       " 'feature_names',\n",
       " 'filename']"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "list(iris.keys())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "print(iris.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, 3:]  # petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)  # 1 if Iris virginica, else 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note**: To be future-proof we set `solver=\"lbfgs\"` since this will be the default value in Scikit-Learn 0.22."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(random_state=42)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "log_reg = LogisticRegression(solver=\"lbfgs\", random_state=42)\n",
    "log_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fa560acd7d0>]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris virginica\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figure in the book actually is actually a bit fancier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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AzOzozz9vlv37zaPntt9lp06ZJ7F69oSnnjJzaUn3hvQ1bNjQ3SG4TM1iNbP1+BZtYdXhVXzy1yf8fOTnxO2VClVicP3BDKw/kDLBZbI1BiFSkxocIe4CX3wBgwaZR9IB6tSBF180HZSTN3kJ4YzrMdeZt2sen275lMOXDwOmX03vmr0Z0mAIrSu0loknRaZJJ+NkJMERIm0nTphBBj//3DRnAYSGwnPPwSuvSI2OcNzxq8eZ8ucU5u6amzgAX7mQcoxuMpohDYdQ2L+wmyMU+YE0UQkhHFK+PEyaBOPGmb46H3xg5szavl2SG+GY/Rf2884f77Dg7wUkaDP0dpsKbXj23mfpVr0bXh7yK0XkHnI3CnGX8fGBJ54wj5P/9hsUK5b02YYNMH++mSaicmX3xZgblCpVCoDIyMgMSuZ/2yO38/bvb7Ns/zI0Gk/lyeN1H2fMfWOoG1rX3eEJYZc0UQkhEnXoYB439/Q0E4OOHWuexrob5aenqDJr55mdvL72dX7850fATOEwuP5g/t3831QsVNHN0Yn8LqtNVNL7SwiRaNo00xkZTE1OjRowfDjcjZUYERERREREuDsMtzh48SCPLnmUhjMb8uM/PxLoHciYZmM4/txxpnedLsmNyBOkBkcIcYejR2HyZJg3z8xy7u8P33xjRkgW+depa6eYuH4i83bNI0En4Ovpy9NNnuaVFq9QLLBYxgcQwoWkBkcI4XKVKpmnrcLDzYjI3t7QtKm7oxLZ5WbsTd5Y+wbV/leN2TtnAzC84XAOP3uYDzp9IMmNyJOkk7EQIk3Vq8O338K5c0mdkWNjTdIzcqSZ+yq/Gj58OAAzZ850cyTZx6ItLPh7Aa+seYXIG6Yd8pHaj/Bm2zepWuQu7Xwl8o0crcFRShVWSn2nlLqplDqhlOqXRjmllHpTKRWhlLqmlFqnlKqdk7EKIZKEhiatz5sHK1bAAw9At25w+LDbwspWs2bNYtasWe4OI9tsPr2Zf33+L574/gkib0TSuFRjfn/ydxb3WSzJjcgXcroGZyoQC4QC9YEwpdRurXV4qnIPA4OBFsAJ4E3gSyD/jJ0uRB41aJCZ12rCBFi5ElavNqMiv/56/prYc8aMGe4OIVtcib7CK7++wswdpmaqZFBJ3r7/bR6v97iMOizylRzrZKyUCgSuAHW01oes274EIrTWr6Qq+zLQSGv9iPV9bWC71tovvXNIJ2Mhcs7Zs/Dqq6ZGB6BCBZg1C9q3d2dUIi1aaxbsWcCLP7/IhVsX8PbwZsx9Y3it5Wsyo7fIlfJSJ+NqQIItubHaDdhreloEVFFKVVNKeQMDgVX2DqqUGq6U2qaU2nbhwgWXBy2EsK9ECZg7FzZvhnr14PhxOHnS3VEJew5dOkT7L9vz+HePc+HWBVqVb8WuEbuYfP9kSW5EvpWTTVRBwLVU264BBeyUPQNsBA4CCcApoJ29g2qtZwIzwdTguCpYIYRjmjaFrVth8WLo3z9pe3g41KqVd6eBWLFiBQDdunVzcySZl2BJ4KPNH/H62te5HX+bIv5FeL/j+wysNzBxIEMh8qucTHCigOBU24KBG3bKjgeaAGWBs8AA4DelVG2t9a1sjVII4TRvbzPysc2RI9C4Mdx/v2m2KlnSfbFlVvfu3YG8O5LxoUuHePKHJ9l0ahMAT9R7gg86fkDRgKJujkyInJGTTVSHAC+lVPLu+fWA1B2MbdsXa61Pa63jtdbzgEJArewPUwiRVUePgp8fhIVBnTpmkMC8pmvXrnTNgyMbWrSFjzZ/RL3P6rHp1CZKBpVkZd+VzO85X5IbcVfJsQRHa30TWAb8RykVqJRqDvTAPB2V2lbgYaVUqFLKQyn1OOAN5NMHUoXIXzp0gL17oVMnuHwZHn0U+vY163nFihUrEpup8opjV47RZl4bXvj5BW7H3+aJek8QPiqcB6s96O7QhMhxOf1M4CjAHzgPLARGaq3DlVLllFJRSqly1nLvYjog7wKuAi8AvbXWV3M4XiFEJpUuDT/9BNOnQ0AALFpkanPWrXN3ZPnTwj0LqT+jPhtPbqREUAmWP7ac+T3nU8i/kLtDE8ItZC4qIUS2O3IEBg6E7dtNh+Q6ddwdUf5xI+YGz/z0DPN3zwegV81ezOw6kyIBRdwcmRBZk9XHxGWqBiFEtqtcGdavh7//TpncXLiQNAVEbmN7yig3/xG4LXIbfZf25fDlw/h7+fNR548Y1nCYPCElBDLZphAih3h6QoMGSe+//BKqVDFzXQnnaK35YNMHNJvdjMOXD1M3tC7bhm9jeKPhktwIYSUJjhDCLX75Ba5fh0cegREj4PZtd0eUktY6V9beXLt9jV7f9GLML2OIt8Tz7L3P8tfQv6hVTB4yFSI5SXCEEG4xfz58+in4+MCMGdCiBZw44e6ocre/z/1N41mN+f7A94T4hvDDYz/wcZeP8fNKdxYbIe5KkuAIIdxCKRg92kz1ULGi6YDcqBH8+qu7I8udvtj9Bf/6/F8cvnyY+iXqs334drpX7+7usITItZxKcJRSu5RSo5VS8tyhEMIlGjSAbdugc2e4dAmefRbi490dlZmiITdM0xATH8OIlSMY+P1AouOjebL+k2wavInKhSu7OzQhcjVnn6IKA/4N/Fcp9T3wudZ6jcujEkLcVQoXhpUr4a23oHdv8MoFz3euXLnS3SFwNuosDy1+iM2nN+Pr6cvUB6YypOEQd4clRJ7g1I8RrfVYpdTrQGfgSSBMKXUWmAPM01rLXMJCiEzx9IQ33ki57d13oU8f85h5Tlu+fHnOnzSZHWd20GNRD05fP03Z4LJ8/9j3NCzZ0K0xCZGXZGmgP6VUYeApzOSYXsAa4EOt9SrXhOccGehPiPxjwQIzgWfhwrBsGbRu7e6Ics7ivYt58ocniY6P5r6y97HskWWEBoW6OywhclRWB/rLdCdjpdS/gHeAV4BIYCJwBFiilPoos8cVQgiAbt3gwQfN/FXt28Ps2e6OKPtZtIXXf3udx5Y+RnR8NIPrD+a3J36T5EaITHC2k3FxpdQYpVQ4sA4oCPTRWlfSWk/SWo8CugNDXR6pEOKuEhwMP/wAL71kOh0PHQovvggJCTlz/pkzZzJz5sycORkQFRtF729689bGt/BQHnzU6SM+7/45vl6+ORaDEPmJU01USqlYzIzes4H5WuuLdsoEAz9ordu6LEoHSROVEPnT7NkwciTExcEDD8DChSYByk45OVVD5I1Iun7dlZ1nd1LQryCL+yymY+WO2X5eIXKznJ6L6n6t9cb0CmitrwM5ntwIIfKvIUOgalXo1QuOHYOcGGB42LBh2X8SYO/5vTyw4AFOXT9F5UKV+bH/j1QrUi1Hzi1EfuZsDc5vQC+t9dVU24OB77XW7VwbnnOkBkeI/O3oUZPcuOOpquyw5ugaen3Ti+sx12lWphk/PPYDxQJz6eyjQuSwnK7BaQ342NnuB7TMbBA55fr165w/f564uDh3hyLuYt7e3hQvXpzg7G5jyYcqVUpa1xr+7/+gUyfo0MF9MWXW/F3zGbpiKPGWePrU6sMXPb/A39vf3WEJkW84lOAopWyDLyigrlLqcrKPPYFOQISLY3Op69evc+7cOUqXLo2/v7/MuCvcQmtNdHQ0ERHmv4skOZn3/ffwwQfw8cfw+ecwcKBrjx8ZGQlAqVKlXHpcrTUT109k4vqJAIxpNoZ3O7yLh5KZc4RwJUdrcLYB2rqstvN5NPCMq4LKDufPn6d06dIEBAS4OxRxF1NKERAQQOnSpYmMjJQEJwt69IAxY+D992HQIDh1CsaONXNcuULp0qUB13YyjkuIY/jK4czbNQ8P5cGnXT5lVJNRLju+ECKJowlORUztzVHgXuBCss9igfNa6xx6eDNz4uLi8PeX6l+RO/j7+0tTaRZ5eMB//wvly5v5q8aNM7ORT5/umqkeSpYsmfWDJHMr7haPfPsIYf+EEeAdwOI+i+laratLzyGESOLQjwGt9Qnrap6uQ5VmKZFbyL3oOqNHQ+nS0K+faao6fx4WLYKs/j1ja6JyhSvRV+i6sCubTm2iiH8Rfuz/I/eWvtdlxxdC3CnDBEcp1QtYobWOs66nSWu9zGWRCSGEgx56CH77zYx8fPw4xMRkPcFxlYjrEXT6qhPhF8IpG1yW1Y+vpkbRGu4OS4h8z5EanCVACeC8dT0tGtPhOE3WuatmAx2Bi8CrWuuv0yhbCfgE8+RWDDBHa/1vB+IVQtyFmjWDjRuhSBEoWNDd0RgHLx6k41cdOXntJLWK1eLnAT9TJriMu8MS4q6QYZOT1tpDa30+2XpaS7rJjdVUTJ+dUKA/MF0pVTt1IaWUD/AL8BsmuSoDfOX417r7tGnThtGjR2fb8QcNGkTXrlnvL7Bu3TqUUly8eMcg2GmaN28eQUFBWT63yP9q14YSJcy61mZ28uPHM3esRo0a0ahRo0zHsi1yGy3mtuDktZM0K9OMjU9ulORGiByUpdnEnTqRUoHAFaCO1vqQdduXQITW+pVUZYcDj2utnRpbJ72B/vbv30/NmjUzFbs7DRo0iIsXL7Jy5cp0y12+fBlvb28KFCiQLXFcu3YNrTUFs/incWxsLJcvXyY0NNThfijR0dHcuHGD4sWLZ+ncuU1evSfzio8/huefh1KlYPVqk/w4IytTNfx69FceWvwQUbFRdKnShW8f/pZAn0CnjyPE3SzbB/rLqN9Nchn0wakGJNiSG6vdmCao1P4FHFdK/QQ0AfYCz2it99iJbzgwHKBcuXKOhppvxMbG4uPjQ+HChbP1PCEhIQ7FkREfHx9K2P7EdpC/v788ASecNmgQLFsGGzZAy5YQFmaasRyV2VHRl+5bSt+lfYmzxDGg7gDmdJ+Dt6d3po4lhMg8R56KWuLg8m0GxwkCrqXadg2wV+VQBngM0wenFBAG/GBtukpBaz1Ta91Ya924WLH8P8S5rano3XffpUyZMpQpY6q8UzdRLVu2jLp16+Lv70/hwoVp3bo1586ds3vMvn370rt37xTbLBYLZcuW5cMPP0xxXps2bdowcuRIxowZQ7FixWjevDkAYWFhVK9eHT8/P1q1asWiRYtQSnHc2k6QuonK1vy0Zs0a6tSpQ2BgIG3btuXYsWOJ57LXRBUWFkbTpk3x9/enSJEidOvWjdu3bwPw1Vdf0aRJEwoUKEDx4sV5+OGHEwfWE3ePkBBYtQq6d4crV6B9e/j5Z8f3z0wT1Re7v+CRJY8QZ4nj+abPM7/nfEluhHCTDGtwtNauejQ8Ckg9qlkwcMNO2Wjgd631TwBKqfeB14GamFofl1AT3fOorh6ftWbB9evXExISwqpVq+xWn589e5bHHnuMt99+m969exMVFcXmzZvTPN6AAQPo3bs3V69eTWyCWr9+PWfOnKFv375p7vfVV18xfPhwNm7ciNaakydP0qtXL55++mmeeuop9uzZw4svvpjh94mJieHtt99mzpw5+Pn5MXDgQEaMGMHPafw2WrVqFT169OCVV15h7ty5xMfHs3r1aiwWC2BqkyZOnEiNGjW4ePEiL7/8Mn379mXDhg0ZxiLyF39/WLoUhg6F+fOhWzdYvNg8deVqn237jJFhIwGY0HoCb7R+Q4YDEMKNXDAclsMOAV5Kqapa63+s2+oB4XbK/g00z7HI8hg/Pz/mzJmDr6+v3c8jIyOJi4ujT58+lC9fHoA6deqkebxOnToRHBzM0qVLGTJkCAALFizg/vvvT7c5qWLFinzwwQeJ71999VUqVarEBx98gFKK6tWrc+jQIcaOHZvu94mPj2fq1KlUr14dgDFjxvDkk09isVjw8Lgzv540aRJ9+vThzTffTNxWt27dxPXBgwcnrleqVInp06dTs2ZNTp8+nVjjJe4eXl4wZw4UKgQffQTvvmtGQbZza6UwYcKEFK/pmfLnFF5a/RIA/+3wX8bcNyZrQQshsizHxsHRWt9USi0D/qOUGgrUB3oA99kp/hXwklKqPbAWeBbzWPn+jOJ1RlZrUtylTp06aSY3APXq1aN9+/bUqVOHjh070r59e/r06UNaTXheXl48+uijLFiwgCFDhhATE8PSpUv55JNP0o0jdfX9gQMHaNKkSYq/Wps2bZrh9/H19U1MbsDM/RMXF8fVq1ft9i3auXMngwYNSvN4O3bsYOLEiezatYvLly8n1nKdPHlSEpy7lIcHTJliJuvs2zfj5AZg4kQzV1R6CY7WmkkbJjF+3XgApj0wjZFNRroiZCFEFuXoODjAKGCO9ViXgJFa63ClVDlgH1BLa31Sa31QKTUA+AwoDuwAumutYx2IN98LDEz/aQxPT09Wr17N5s2bWb16NbNnz+bVV19l/fr11KtXz+4+AwYM4L777iMiIoK//vqL2NhYHsqgHj91HFrrTFXJe6UaV992DFuTkzNu3rxJp06daN++PV9++SXFixfn4sWLtGzZkthYuX3uZkrBM8lmzLNY4JdfzGzk9owfPz7d42mtefnXl/nvpv/ioTyY030OA+u7eMZPIUSm5eg4OFrry1rrnlrrQK11Odsgf9akJkhrfTJZ2WVa6ypa62CtdRuttb2mLJEGpRTNmjVj/PjxbN26lVKlSrF48eI0yzdt2pTKlSuzcOFCFixYQM+ePZ0ee6ZmzZps3bo1xbYtW7ZkKv70NGjQgDVr1tj97MCBA1y8eJHJkyfTqlUratSowfnz510eg8j7nn0WOneGN980Y+akNmHChDRrbyzawugfR/PfTf/Fy8OLRb0XSXIjRC6Tk31wRA7ZvHkzv/76K506dSI0NJSdO3dy6tQpatWqle5+/fv35/PPP+f48eN89913Tp93xIgRTJkyhTFjxjBs2DDCw8OZMWMG4Nq5l8aOHUu3bt2oUqUK/fr1Q2vN6tWreeqppyhXrhy+vr7873//4+mnn2b//v2MGzfOZecW+Ufjxqapatw4iIqCt992bCbyeEs8Q5cPZf7u+fh6+rLkkSUyaaYQuZDTT0gppRoqpb5QSm2zLl8qpRpmR3Aic0JCQvjjjz/o2rUrVatW5aWXXmLcuHEMGDAg3f0GDBjAwYMHCQkJoUOHDk6ft3z58ixdupTly5dTr149Pvzww8Rqfj8/v0x9F3seeOABvvvuO3766ScaNGhA69atWbt2LR4eHhQrVoz58+fz/fffU6tWLSZOnMiUKVNcdm6RfwwaBF9/bTohv/uuqdFJ3iq6fft2tm/fnmKf2IRY+i3tx/zd8wnwDiCsX5gkN0LkUk6NZKyU6g98gZlC4U/r5n8B7YBBWmu3TqeQH0cyzus+/vhj3njjDa5cuWL3iai7mdyTucOKFdCnD8TGwpNPwqxZ4Ol550jGt+Nv8/C3D7Py0EqCfYP5sd+PNC8nD3sKkV2yfSTjVN4CxmmtJ6cK4lXgTWS+qLve1KlTadKkCcWKFWPz5s1MmjSJQYMGSXIjcq1u3cwoxz16wNy5UL48jB8PDRsmVUzfjL1Jj0U9WHNsDYX9C7N6wGoalcr8PFVCiOznbIJTDPjGzvZvAenoIDh8+DCTJ0/m0qVLlClThhEjRvDGG2+4Oywh0mUb5XjsWNNUBSQ2T127fY0Hv36QP079QWhgKL8+8St1iqc9rpQQIndwNsFZC7QBDqfa3gZY74J4RB734YcfJk7vIERe0qIFrFuX1NE4IQEirlzkoWWd2HFmB2WDy7LmiTVULVLVrXEKIRzj7GSbPwFvK6UaA7ax//8F9AImuDw6IYTIQbbkxmKBJwbf4vvfT3LrkcNULlmZNU+soXzB8u4NUAjhMEcH+kstcQbvZD4FpmU5IiGEcLMdh0/z9TINUQ3x+/oPvl9fhPIFS7o7LCGEExwd6M+RJcOB/oQQIrc7cvkIvX9sDkNaQvARbp+sQ99uJTl71t2RCSGcIY+2CCGE1b4L+2g5tyUnr52kUfWirPvZQs2asHcvtGoFp065O0IhhKOcHslYKVUY6AyUA3ySf6a1/o+L4hJCiBy148wOOn7ZkUvRl2hToQ3LH1tOAd8CrF8PHTvCrl3QsiWsXQsVK7o7WiFERpxKcJRS/wLCgBjMI+MRQEnr++OAJDhCiDznz1N/0mVBF67FXOOBqg+w5OEl+Hv7A1CsGPz2G3TpYp6sKlLEzcEKIRzibBPVf4EFQGngNmYE43LANuBd14Ymcrs2bdowevTobDv+oEGD6No168Pgr1u3DqUUFy9edHifefPmOT3ZqMibfjv2Gx2+7MC1mGv0rtmb7x79Dn9vf4YPH87w4eZZikKFzMzjP/8MwcFuDlgI4RittcMLcA2oZl2/CtS0rjcB/nHmWNmxNGrUSKdl3759aX6Wmw0cOFADetKkSSm2r127VgP6woULDh+rdevW+umnn3bonA8++GCG5S5duqSvX7/u8PmddfXqVX3lypUsHycmJkafOXNGWywWh/e5deuWPnfuXJbPnZ68ek/mJysPrtS+k3w1E9CPL3tcxyXEJX4GaPMj8k4JCVqPGqX1n3/mVKRC3H2AbToLOYGzNTixydbPAbZBIaKAUplLsURG/Pz8eO+997hw4YK7QwEgNtbcBoULF6ZAgQLZdp6QkBAKFiyYYRwZ8fHxoUSJEk7NaO7v70/x4sUdLi/yniX7lvDQ4oeISYhhRKMRzOs5Dy+PpFb7GTNmMGPGDLv7fv45TJsGHTqYwQGFELmPswnODkxtDcA64E2l1EDgE+BvF8Ylkmnbti0VKlRg0qRJ6ZbbsGEDTZs2xc/Pj9DQUF544YXEJGDQoEGsX7+eqVOnopRCKcXx48cdOr+tqejdd9+lTJkylClTBriziWrZsmXUrVsXf39/ChcuTOvWrTl37pzdY/bt25fevXun2GaxWChbtmziSMipm6jatGnDyJEjGTNmDMWKFaN5czPRYVhYGNWrV8fPz49WrVqxaNGiFN8vdROVrflpzZo11KlTh8DAQNq2bcuxY8cSz2WviSosLIymTZvi7+9PkSJF6NatG7dv3wbgq6++okmTJhQoUIDixYvz8MMPExER4dD1FTnvi91f8OiSR4mzxPHiv15k2oPT8FApfxwmb6JKbfBgGDAAoqJM35yffsqJqIUQznA2wRkLRFrXXwcuYAb4K8SdA//lCUqlvcycmVRu5sz0yybXqJFj5Rzl4eHBO++8w2effcaRI0fslomIiKBLly40aNCAnTt3Mnv2bBYuXMirr74KmFm9mzVrxpNPPsmZM2c4c+YMZcuWdTiG9evX8/fff7Nq1SrWrFlzx+dnz57lscceY+DAgezfv58NGzbw+OOPp3m8AQMGEBYWxtWrV1Oc48yZM/Tt2zfN/b766iu01mzcuJEvvviCkydP0qtXLx588EF2797Ns88+y7///e8Mv09MTAxvv/02c+bM4c8//+Tq1auMGDEizfKrVq2iR48edOjQge3bt7N27Vpat26NxWIBTG3SxIkT2b17NytXruTixYvpfg/hPtO3Tmfg9wOxaAtvtHqD9zu+71TtHoCXF8yfD8OHw+3bZqLOZcuyKWAhRKY49RSV1npbsvULQBeXRyTseuCBB2jevDljx45l0aJFd3w+bdo0SpYsybRp0/Dw8KBmzZq88847PPXUU0yaNImQkBB8fHwICAigRIkSTp/fz8+POXPm4Ovra/fzyMhI4uLi6NOnD+XLm5bLOnXSnpCwU6dOBAcHs3TpUoYMGQLAggULuP/++9ONr2LFinzwwQeJ71999VUqVarEBx98gFKK6tWrc+jQIcaOHZvu94mPj2fq1KlUr14dgDFjxvDkk09isVjsznw+adIk+vTpw5tvvpm4rW7duonrgwcPTlyvVKkS06dPp2bNmpw+fTqxxku43webPmDML2MAeK/9e/xf8/9Ls+yKFSsA6Natm93PPTzgs88gIAA++ggeeQTmzTM1O0II98vUQH9KqcpKqa7WpZKrg8pJWqe9JK+dHj48/bLJbd/uWDlnvffee3z77bds27btjs/2799Ps2bNUvxybtGiBbGxsRw+nHpuVOfVqVMnzeQGoF69erRv3546derQu3dvpk+fnm6fIS8vLx599FEWLFgAmBqVpUuXMiCD3w6NGjVK8f7AgQM0adIkxV/gTZs2zfD7+Pr6JiY3AKVKlSIuLi5FjVJyO3fu5P7770/zeDt27KBHjx6UL1+eAgUK0LhxYwBOnjyZYSwi+2mtmbhuYmJyM/WBqekmNwDdu3ene/fu6ZZRCqZMgddfN4+Qf/aZeRVCuJ9TCY5SqohS6nvgH+B76/KPUuoHpVSGo0MopQorpb5TSt1USp1QSvVzYJ/flFJaKeX0oIT5TZMmTejduzcvv/zyHZ9prdOsZne2+t2ewMDAdD/39PRk9erVrF69mrp16zJ79myqVq3K7t2709xnwIABrF+/noiICMLCwoiNjeWhhx5yKo70vnd6vLxS3k62Y9ianJxx8+ZNOnXqREBAAF9++SVbt25l1apVgOMdoUX2sWgLz696ngnrJ+ChPJjXYx6jmozKcL+uXbs6NEyBUjBpEsyeDStXgqdMWiNEruBsDc7nQBWgJeBnXVoBFYFZDuw/FfMkVijQH5iulKqdVmGlVH8yMdpyfjZ58mQ2btyY+AvUplatWvz5558pfkH//vvv+Pj4ULlyZcA8TZSQjX9eKqVo1qwZ48ePZ+vWrZQqVYrFixenWb5p06ZUrlyZhQsXsmDBAnr27On02DM1a9Zk69atKbZt2bIlU/Gnp0GDBnb7HoGpRbp48SKTJ0+mVatW1KhRg/Pnz7s8BuG8uIQ4nvjuCT7Z8gneHt4s7rOYgfUHOrTvihUrEpupHDF4MNge+ouPh0WLsl5rK4TIPGcTnE7AMK31H1rreOvyB/CU9bM0KaUCgd7AOK11lNb6d2A5YLcnqlIqBBgPZNxj9C5SpUoVhg8fzscff5xi+6hRo4iMjGTUqFHs37+fsLAwXnnlFUaPHk1AQAAAFSpUYMuWLRw/fpyLFy9mqrYiLZs3b+bNN99k69atnDx5kuXLl3Pq1Clq1aqV7n79+/fn888/JywsLMPmKXtGjBjBkSNHGDNmDAcPHmTZsmWJj/a6oubKZuzYsXz77be8/vrr7Nu3j/DwcD788ENu3bpFuXLl8PX15X//+x9Hjx4lLCyMcePGuezcInNuxd3iocUPsWDPAgK9A/mx/4/0qdUnR8799NPQty+MHi1NVkK4i7MJzgXgpp3tt4BLGexbDUjQWh9Ktm03kFYNzmRgOpDuHL5KqeFKqW1KqW25ZZyY7PbGG2/c0cRSunRpfvrpJ3bu3En9+vUZPHgwffv2ZfLkyYllxowZg4+PD7Vq1aJYsWIu7R8SEhLCH3/8QdeuXalatSovvfQS48aNyzBpGTBgAAcPHiQkJIQOHTo4fd7y5cuzdOlSli9fTr169fjwww8ZP348YDpGu8oDDzzAd999x08//USDBg1o3bo1a9euxcPDg2LFijF//ny+//57atWqxcSJE5kyZYrLzi2cd/X2VTp+2ZGwf8Io4l+E3wb+RvtK7XPs/J07g6+vGSunXz+IicmxUwshrJR2og5VKTUE07T0uNY6wrqtNDAfWKS1/jydfVsC32qtSyTbNgzor7Vuk6psY0xzWGOgDHAM8NZax6cXX+PGjbW9DrhgOuHWrFkzw+8o8r6PP/6YN954gytXrth9Iiq3kHsye5y5cYbOCzrz97m/KRNchtUDVlOzmPPX2VYD6MzPyOTWr4fu3eH6dWjf3jxGno3jYgqR7yiltmutG2d2/wz7tyil9mCGLLepCBxXStlGMbPNS1Uck5SkJQpIPYtLMHAj1fk8gGnAc1rreFc2M4j8aerUqTRp0oRixYqxefNmJk2axKBBg3J1ciOyx9ErR+nwZQeOXjlK9SLVWf34asqFlHNLLK1bmySnc2f49Vdo1w5+/NFM3imEyH6OdOBd4qJzHQK8lFJVtdb/WLfVA8JTlQvG1NwstiY3tmcSTiulHtZab3RRPCKfOHz4MJMnT+bSpUuUKVOGESNG8MYbb7g7LJHDdp/dTecFnTkbdZZGJRvxU/+fKBaY+WwiszU3ydWvD3/8AR07wrZt8NprMMuRxzGEEFnmVBNVlk+m1CJMbdBQoD7wI3Cf1jo8WRmFecrKpiywBdNUdUFrneZzt9JEJfISuSdd59ejv9JrcS9uxN6gbYW2/PDYDxTwzT3tQWfPwiuvwKefSjOVEI7K9iaqNE7aDqiFSVbCtdbrHNx1FDAHOI/plDxSax2ulCoH7ANqaa1PkqxjsVLK1lP0XEZ9cIQQd58vd3/J4OWDibfE80jtR5jfcz5+Xq7rYO4KJUqYUY5tYmJgzx5onOkf3UKIjDiV4Fg7FH8HNCJpTqpSSqltwENa68g0dwa01peBnna2nwTsDoCitT4OuKQjTmYHhRPC1XKy5jS/0lozeeNkXl/7OgAvNXuJ9zq8d8ekmZllm6LBmbFwHKE1DB0KixfDnDkytYMQ2cXZGpxPgASgitb6GIB1qoavrJ/lzCATmeDt7U10dHTimDBCuFN0dDTe3t7uDiPPirfEMypsFLN2zEKh+LjzxzzT9BmXnmPlypUuPZ6N1lC0KMTFweOPw/HjMHZs5ifjFULY52yC0wFoY0tuALTWR5VSzwL2h3nNJYoXL05ERASlS5fG399fanKEW2itiY6OJiIigtDQ0Ix3EHeIio3i0SWP8uM/P+Ln5cfXvb7moZrpT/GRGcuXL3f5McFM0vnhh1ChArzwAowbB8eOmXmsJOcVwnVcNQ2C64bEzSbBweYJddus10K4i7e3N6GhoYn3pHBc5I1IeizqwbbIbRTxL8Lyvsu5r+x92XKutGYRd5XnnoPy5c1AgHPmwKlT8O23EBKSracV4q7h7EB/3wHFgL5a61PWbeWABZgnnHplS5QOSu8pKiFE3rbjzA66L+xOxI0IKhWqxE/9f6JakWruDivLtmyBbt3g/Hl46SV4/313RyRE7pDVp6ic7Y33LBAAHLXOBn4cOGLd9mxmgxBCiPQs2beEFnNaEHEjgpblWrJ5yOZsT25mzpzJzJkzs/UcAPfeC3/+Cf37w3/+k+2nE+Ku4WwNTgBmNvC2QA3M0037tNa/Zk94zpEaHCHyF601b218i3FrzeSlT9Z/ks+6foaPp0+2nzurUzVkxc2bsHo1POT6rkVC5Bk5Ng6OUsoTuAbU01r/AvyS2ZMKIURGouOiGbJ8CAv3LkSh+G+H//Jisxdz7AGBYcOG5ch5UtMannzS9Md58UV4913wclVvSSHuIg7/t9FaJyilTgDZ/6eTEOKudvr6aXp/05stEVsI8gliYe+FdK3WNUdjyInmKXuUgg4d4LvvYMoUCA+HRYugYEG3hCNEnuVsH5xJwDtKqaLZEYwQQqw7vo5GMxuxJWIL5UPKs2nwphxPbtxt2DBYs8aMl/Pzz9C0KRw44O6ohMhbnE1wxgAtgAil1BGl1N/Jl2yITwhxl9Ba8+GfH9L+i/acv3me9pXas234Nu4Jvcct8URGRhIZme7g7NmqVSvYuhXq1oVDh6BJE9NsJYRwjLMtu0sw80/JKHlCCJeJio1i6PKhLA5fDMCrLV5lUttJeHp4ui2m0qVLA+6dVqNCBTMbuW1qh1Wr4OGH3RaOEHmKQwmO9emp/2LmkfLGjFr8jNb6YvaFJoS4Gxy6dIhei3sRfiGcIJ8g5vecT6+abh1SC4CSJUu6OwQAgoJg4UJ48EHok2wyHK1legch0uNoE9VEYBAQBiwE2gPTsykmIcRd4qu/v6LhjIaEXwinRtEabB22NVckN+D+JqrklDLzVvn7m/c3bkDbtrB2rXvjEiI3czTB6QUM0VoP11o/BzwI9LQ+Oi6EEE6Jio1i0PeDePy7x7kZd5PH6jzGlqFbqFG0hrtDyxM+/RTWr4f27eGNNyA+3t0RCZH7OJrglAU22t5orbcA8UCp7AhKCJF/7T67m8YzGzN/93z8vfyZ1W0WX/f6mgK+BdwdWp7x8svw+uummWrSJGjd2sxKLoRI4miC44kZwTi5eFw3WacQIp/TWjNt6zSaft6Ug5cOUrtYbbYO28rQhkNzbPA+ZzRq1IhGjRq5Owy7PD1NYrNmDZQuDZs2Qf368M037o5MiNzDoakalFIWzMjFMck2dwHWA7dsG7TW3V0doDNkqgYhcqfIG5EMWT6EVYdXATCs4TA+6vwRAd4Bbo4sbe6cqsEZly7BkCHwww/m/V9/mfmthMjrcmqqhvl2tn2V2ZMKIe4ei/YuYlTYKK7cvkIhv0J81vUzHqn9iLvDylBe+WOpSBEz6vGMGbB3ryQ3Qtg4Ndlmbic1OELkHpduXWLUj6P4Jty0m3Su0pnZ3WdTqoB03csJW7fCl1/C229DYKC7oxHCeVmtwXF2JGMhhMjQ8oPLqTO9Dt+Ef0OgdyAzus7gx34/SnKTQ7Q20z18+inUqwcbN2a8jxD5TY4mOEqpwkqp75RSN5VSJ5RS/dIoN1AptV0pdV0pdVop9Z5SSjo0C5HLnblxhj7f9KHHoh6cjTpLy3It+Xvk3wxvNDxXdiROz4QJE5gwYYK7w8gUpWDuXDPNw5Ej5imr55+HqCh3RyZEzsnpGpypmKexQoH+wHSlVG075QKA54GiQFPgfsw8WEKIXMiiLczYNoOaU2uydP9SAr0D+ajTR6wduJZKhSo5fJwJEyZQp04dh8oeP34cpVS29ZWZOHEiEydOtPtZhQoVeP/997PlvK4wevRoXnihDVu3wrhx4OEBH38MNWvC99+bGh4h8rscS3CUUoFAb2Cc1jpKa/07sBx4PHVZrfV0rfVGrXWs1joCWAA0z6lYhRBJBg0ahFIKpRTe3t4UL16ctm3bMnXqVOLi4gg/H07rea0ZETaCazHXeLDqg+x7eh/P/es5p+eSGjNmDOvXr3eobNmyZTlz5gz169fPxLfK2Pjx4xk/fny2HDun+PjAf/5j+uM0bgynT8PgwXDtmrsjEyL75WSzTzUgQWt9KNm23UBrB/ZtBYTb+0ApNRwYDlCuXLmsxiiEsKN9+/Z8+eWXJCQkcOHCBX777TfeGP8Gb376Juf7nMfibSE0MJRPunzCw7UeznRzVFBQEEFBQQ6V9fT0pESJEpk6jyPyavOUPQ0awObN5kmrAgWgYEGzPcY68Iev7537xMXF4e3tnWMxCuFqOdlEFQSk/rvhGpDu8KVKqSeBxoDd+mCt9UytdWOtdeNixYq5JFAhREq+vr6UKFGC0qVLU7deXULahKAHas7+cxbL7xZGNBrB/qf307NqT1555RXKlClDYGAgTZo04eeff05xrAMHDtC9e3dCQkIICgqiWbNm7NmzB7iziWrPnj3cf//9BAcHU6BAAerVq8da6wRM9pqoNmzYQNOmTfHz8yM0NJQXXniB2NikMUrbtGnDqFGjeO211yhatCjFixdnzJgxWCwWp69JVFQUAwYMICgoiBIlStzRZHXy5EkeeughChQoQIECBejVqxenT59O/Nxec9y8efNSJHi2MosWLaJy5coUKFCAnj17cvFi0jzHCQkJjBkzhkKFClGoUCGef/55EhISUhx31apVtGnTkrFjC/Hcc4Xp1KkT+/fv58MPoXZtmDnTXMuFCxfSrl07/P39mTZtGsHBwSxZsiTFsX755Re8vb05d+6c09dMiJyUkwlOFBCcalswcCOtHZRSPYF3gC4yc7kQ7vfHyT9o+nlThq4YypXgKxSuW5jKZyszvet0CvkX4sknn2T9+vV8/fXX7Nmzh4EDB9KtWzd2794NmAksW7RogVKKX375hR07dvD000/f8QvZpl+/fpQsWZItW7awc+dOJkyYgJ+fn92yERERdOnShQYNGrBz505mz57NwoULefXVV1OUW7BgAV5eXmzatIn//e9/fPTRRyxevPiO423fvp3t27eneS2mTJlCzZo12bFjBxMnTuS1115j2bJlgBkcsGfPnpw7d47ffvuNtWvXEhkZSc+ePZ0eOPD48eMsXryY7777jtWrV7Nz507Gjh2b+PkHH3zArFmzmDFjBn/++ScJCQksWLAgxTFu3rzJ888/z5YtW1i3bh0hISF069aNpUtjOXIEnnrKlBsz5lVGjRrFvn376N27N3379mXOnDkpjjVnzhy6du1KaGioU99DiByntc6RBQjEdDCummzbF8A7aZTvDFwA7nX0HI0aNdJCCNcaOHCgbt2hte6+sLtmApoJ6NIflNZf//21/ve//639/f211lofPnxYK6X0iRMnUuzfo0cPPXLkSK211q+99pouV66cjomJsXuu8ePH69q1aye+L1CggJ43b57dsseOHdOA3rp1a+KxK1eurBMSEhLLzJ07V/v4+OibN29qrbVu3bq1/te//pXiOO3bt9dDhgy54/iANj8i71S+fHndvn37FNuGDBmimzdvrrXWevXq1drDw0MfO3Ys8fMjR45opZT+5Zdf7H5XW7yBgYEproevr6++evVq4rY333xTV65cOfF9yZIl9Ztvvpn4PiEhQVetWlW3bt3abuxaax0VFaU9PDz02rUb9SefaB0cbK6lUu/rYcO0Pn3alNu6dav29PTUp60bLl++rP38/PSKFSvSPLYQrgJs01nIO3KsBkdrfRNYBvxHKRWolGoO9AC+TF1WKdUO07G4tzYTewoh3OD09dNsOrWJ9SfWs/zgcgK8AxjXahwHRh+g7z19gaQpDXbs2IHWmlq1aiX2pQkKCiIsLIwjR44AsHPnTlq0aIGPj49D53/xxRcZOnQo7dq146233uLAgQNplt2/fz/NmjXDwyPpx1qLFi2IjY3l8OHDidvq1q2bYr9SpUpx/vz5O47XsGFDGjZsmOb5mjVrdsf7ffv2JcZSqlQpKlSokPh5pUqVKFWqVGIZR5UvX56QkBC78V67do0zZ86kiMXDw4OmTZumOMaRI0fo168flStXJjg4mNDQUCwWC5GRJ3nmGTMzOYBSjZk1C6pUgQMHoHHjxtxzzz3Mn28Gs//6668pVKgQXbp0ceo7COEOOf2Y+CjAHzgPLARGaq3DlVLllFJRSilbL+FxQAjwo3V7lFLqpxyOVYi71tmos4xZPYaqn1bln0v/oFCMajyKI88e4T9t/0OQj+knsm/fPipVMo+BWywWlFJs3bqVXbt2JS779+9PbObQTjbPTJgwgX379tGzZ082bdpE3bp172gysdFap9m5Ofn21B1nlVJ2++Bk1ESVHkdi8fDwuON6xMXF3VHe0XjT061bNy5cuMCMGTP466+/2LlzJ15eXon9k2ydjhctCqR3b2jYEKpXN9uGDh3K3LlzAdM8NWjQIDw9nXs6Tgh3yNHB87TWl4GedrafxHRCtr1vm4NhCSGsIm9E8t4f7zFj+wxux98GoELBClQoXoGpD05NUXbv3r2sWrWK119/HYAGDRqgtebs2bO0bWv/v3DDhg356quviI2NdbgWp2rVqlStWpVnn32WkSNH8vnnnzN48OA7ytWqVYtvvvkGi8WSWIvz+++/4+PjQ+XKlR2+Bo7avHnzHe9r1qyZGEtERATHjx9PrMU5evQokZGR1KpVC4BixYpx7ty5FMnQrl27nIohJCSEkiVLsnnzZtq1aweY5GrLli2ULFkSgEuXLrF//36mTp2a+O+yY8cO4uPj7zhexYqwZAlER5vBAgGaNh3A4cP/R9eu/2PHjh0sWrTIqRiFcBeZqkEIwclrJ3nmx2eo9HElPv7rY27H36ZnjZ5sH76d1hVa46W9OHv2LJGRkezevZspU6bQpk0bGjVqxJgxZgzOatWq0b9/fwYNGsSSJUs4evQo27Zt4/3330/sfDtq1CiioqJ45JFH2Lp1K4cPH2bhwoV2f7FHR0fz9NNPs27dOo4fP85ff/3F77//npggpDZq1CgiIyMZNWoU+/fvJywsjFdeeYXRo0cTEOD6Wcs3b97M22+/zT///MOsWbP44osveOGFFwDzWH29evXo378/27dvZ9u2bfTv35+GDRsmJiJt2rTh8uXLTJ48mSNHjjB79uw7nlhyxHPPPcd7773HkiVLOHjwIM8//zxnzpxJ/LxQoUIULVqUWbNmcfjwYdavX8+IESPw8kr771t//6T15ctDgIcJC3sJT89WzJlTFXmASuQJWenAk9sW6WQshHO2RmzVjy15THtO9EzsQNx7cW+988zOxDIDBw5M7HDr6empixQpolu3bq0/+eSTOzoLx8bG6vHjx+uKFStqb29vHRoaqrt166a3bduWWGbv3r26S5cuOjAwUAcFBelmzZrpPXv2aK1TdryNiYnRffv21eXKldM+Pj66ZMmSetiwYfratWta6zs7GWut9fr16/W9996rfXx8dPHixfXzzz+vb9++nfh569at9dNPP50i5oEDB+oHH3zwjmtTsmRJXbJkSbvXrXz58nr8+PH6scce04GBgbp48eL6nXfeSVHmxIkTukePHjooKEgHBQXpnj176lOnTqUo89lnn+ly5crpgIAA/eijj+qPPvrojk7GGXVEjouL088//7wOCQnRISEhevTo0XrEiBEpOhmvWbNG165dW/v6+uratWvrVatW6cDAQD137tw0r6WNxaL1hx+ut94D8zVo7een9ejRWh89avfyCOESZLGTscwmLsRdJsGSwMpDK/ngzw/YeNLMwuipPHmk9iO81vI16hR3bKqE/M7WbJSffkZm1uLFi3nqqadYvjySDz8M4PvvzfZhw2DmTLeGJvKxrM4mLhNYCnGXuHjrIvN2zWPG9hkcvmyeKgr2DWZ4w+E80/QZyoXISODJRUREuDsEt7t16xbHjx9n8uTJDBs2jFatAmjVCvbuhffeg2efTSr7009w6hQMGADZ0CIohNOkBkeIfExrzYYTG5ixfQZL9y8lNsE8NVM+pDzPNX2OIQ2HEOybevxNIYwJEybw1ltv0aJFC3744QeCg9O+V/71L/jrL/NEVr9+MGSIeRpLiMzKag2OJDhC5EMR1yNYuHchs3fO5sBFM3aMQtGlaheeavQUD1R9AC8PqcAVrqE1LFpkZiz/66+k7fXrm0Snf38oVMht4Yk8ShKcZCTBEXez6zHXWbpvKV/t+Yq1x9aiMf+3SwaVZEiDIQxtOJTyBctnexxnz0J8PJQpk+2nylbDhw8HYKZ0MnHK7t0wZw589RVcvmy2zZxp+usI4QxJcJKRBEfcbW7E3OCnwz+xdP9Slh9cnjh2ja+nL92qd2PAPQN4oOoDeHtmz6zQcXHmF9qmTfDrr/Dnn3DtGhQrBnm9C4t0Ms6a27fhhx9MorNgAdhat15+GSIjoW9f6NABZMJykRbpZCzEXebirYusOLiCZQeW8cuRX4hJiEn8rHX51jxe93F61+pNQb+CLj/3uXMmidmwAdasMcP5+/qaROf27aRy0dEuP3WOmzFjhrtDyNP8/ODRR81ik5AAc+fChQsm8SlUCB54ALp3h86dk5IgIVxBanCEyOW01uw9v5dVh1fx0+Gf2HBiAwnazL6tUNxX9j561exFn1p9XPokVFwc/P13ytqZ69dNQnPjhul3kZZChZKaJ4RI7vBhWLwYFi6E8PCk7d7eMH266bMjBEgTVQqS4Ij84nL0ZX49+iurDq/i5yM/E3kjMvEzLw8v2lVsR68avehRowclgkq49NyrV8P//R/s32+Smfj4lLUzd5P+/U1Ng8geBw/CihWwfDn88YdJpm3zhM6dC9u2mWastm0h2Xyj4i4hTVRC5AMXbl5gw4kNbDixgfUn1vP3ub8TOwmD6SjcuUpnOlXuRMfKHSnkn32PpBQqBJUrw/nzphbGzw9iYtKvsbGnbNnsiS+n3Lq1wvqdu7k7lHyrenWzjBkDFy9C4cJJny1YYJpBp00DDw+4915o3x5atjSPpEtzlsiI1OAIkcMs2sKhS4fYGrGVTac2sf7EevZf3J+ijI+nD83LNqdzlc50rtKZe4rfk+bs1NnpwgXYvDmpz014eFKtTnr9bPJDE5V0Mnavv/6CVatM8+jmzeaes0les3brlrnX8vpTe+JOUoMjRC6mtSbiRgRbIrawNWIrWyK3sC1yG9djrqco5+/lz31l76NV+Va0Kt+KpqWb4u/tn8ZRc06xYtCtm1nA/JLZsydlv5wrV0wtT0b9cvKarl27ujuEu1rTpmYZP97cW+vXw9q1pimrTZukcr/8Aj17QsmS0KhRyqVUKXdFL3IDqcERwkVuxd0i/Hw4f5/7mz3n95jl3B4u3LpwR9nSBUpzb+l7aVq6Ka3Kt6JRqUb4ePq4IeqsO3/+zlqecuVMZ1Ihstvs2fDSS2Z4gtRKl4ajR8HH+l/r6FGzzdc3Z2MUmSOdjJORBEdkN60152+e55/L/3Do0qHEZc/5PRy5fCRFvxmbgn4FaVKqCfeWvpcmpZrQpHQTShXIv39a2jolBwW5OxJxt7BY4MgR2L7dLNu2wY4dJpnZty+pXPHicOkSVKkCdepA7dpQqxZUrWr6Ask9m7tIgpOMJDjCFWLiYzh1/RQnrp7gxLUTnLh6gn8u/5OY1KRuXrLx8vCiRtEa3FP8HrOE3kPd0LqUDS7rlv4zQtzNLBbTcbl4cfM+KsrMjXXkiPkstWnTYORIs/7HH6bpq0oV0+G+bFnTBObpmXPxC+mDI4RTbsXd4syNM5yNOsuZqDOcuXGGk9dOcuLaicTXs1Fn0z1GiG8I1YpUo1qRalQtXJWqRapSp3gdahStkWebmcSdpJNx3ubhkZTcgKmdOXTI1C4eOGCaUsPDzXAIR45AjRpJZX/5BSZOTHk8T0/Tp6dmTfj556Tta9aYCUZDQ835fORHQK4hCY7I06LjorkcfZlL0ZfM6y3zevHWRc7dPMeZKGsyY01qbsTeyPCYnsqT0sGlKR9SnvIFy1MuuBxVCldJTGqKBhSVGhkh8ig/PzMJaP36aZdp184MdHn4sOm3c+qUGcX71CkIDExZ9qGHTCdom8KFTbITGgrPPAO9epntJ0+aaU2KFDFlChUyiyRE2UcSHOE2cQlxXI+5zo3YG1yPuW7WY5Ktp9p+5faVO5KZ6Hjn5gTw8fShZFBJSgSVSFzKhZSjXEi5xISmVIFSMtO2kJqbu1irVmZJLiYGTp82TV02sbFmXJ7Tp01ne9vYUZcvm5qhfv2Syv78M1jnb00hKMgkPIcPJ83L9e675hjBwVCgQMqlcmXTdAZm6guLRebzSkuO/hRXShUGZgMdgYvAq1rrr9Mo+wLwMuAPLAVGaq1j7JXNelxpf+boz7isHsMdMWitibPEEZsQm7jcUz+Wi1diwTP5EkPBorF8vSipXExCDNFx0dyKu0V0vPU1Lpqps24RHXcLvKPB+xZ4mVcv/1tUrpFUPio2KnFiyKzw9vCmSEARivgXoUhAEQr7F6aIv3m1JTDJE5qCfgVzrPYlN9xXrjhGbojBFcdwRQwlSpi/5FMLDTWzqOfUMUTO8/U1yUVyPj4QFpb03mIxnZjPnTNL9epJn4WGQpcuJnG5ciUpEYqKMvdf8iRl3jzTjGbP6NHw6adm/a+/oHlzE5stAfL3h4AA8/rFF1Chgik7Z47peG37LPlSrpyZCwxM0rRxo/lutsXbO2m9aFGzDyT9v8mtFdo5/WfqVCAWCAXqA2FKqd1a6/DkhZRSnYBXgHZAJPAdMNG6LU3XYq4RdigMjcaiLWitU6xbtAWNvmOduhZQGpQF0CnWZ27PeH+LtsB99vdHaf6z3v7+Fm0hQSeQYEmAzvHgkQAqATxSrj+2JIEEnUC8JZ4Ei/XVul/ydYbFW/exHiPZscp9GJ+YzMTExxCbEEucJe7Oi/i4/Wt7FXjAbiqaSh37m+OBg5dSbvNQHgT7BhPsG0wBnwKJ66nfF/A16yG+IXckM4HegdJcJHKMvcQkve3ZdQyRO3l4mLGjihUzT2kl1727WZKzWEzz1vVUzy289pqpFbpxI+Vy/bp58ssmOtr0DYqJMcvFiymPk3xwxJ9/hm++sR93mzZJCU5UlJkaIy0LF8Jjj5n19983s8MnT4ZsCVHBgqZJzqZHDzhzxsTr5ZW0eHrCI4/A4MGmXHg4TJ5sPsuqHHuKSikVCFwB6mitD1m3fQlEaK1fSVX2a+C41vo16/v7gQVa63Qn3VGllOapbAk/3/L28MbH0ydxORfpAwnWJd43aT3Bh84dfVKUDfAKwN/bnwDvAPy9zOu/X/SHuADrYl2PN6/7dlvLevsT6B1IgHdAvk5OckOthSuOkRticMUxnN2/m3V0wxUrVrgsBlcdQwgbrU2iY0uCoqOTlqZNTZ8jMHPMHTxott+6lVTm1i1T0/R//2fKXbtmkpHYWPvLjBnw4IOm7OTJMHas/bhSj2ZesSIcP26/7MsvwzvvmPVffoGOHW2f5JHHxJVSDYBNWmv/ZNvGAK211t1Sld0NTNZaL7a+LwpcAIpqrS+lKjscGA7gV9qvUdt32+KhPFBKoVCJ6x7KA4VKsW777OsFCrQHaOsrKnF92LD097WtT5mS7BikPN64cfZj8VAeeHp44qk8GfOiF2hPsHiCJeX6wq9NGS8Pr8Ty9tabN/O07udl9k22fuyoJ76evikSFB9PnzsSjNzwyzC/yC2/DHPDv2luOIaz+9t7iio3fA8hcpOEBNMhO3UipLVJamz27DEJVXy82Sc+PmmpWDHpKbYzZ+C338z2QYPyToLTEvg2eS2MUmoY0F9r3SZV2SPA01rrVdb33pimrYpa6+NpnSOz4+Dkhh9auSEGVxxDfngnyQ3/Hq44Rm6IwRXHcHZ/W82NrSbHFTG46hhC3A3y0jg4UUDq+V+DAXvP7aYua1vP+BlfIYRwgeSJjRAi78nJBOcQ4KWUqqq1/se6rR4QbqdsuPWzb5KVO5e6eSq17du3RymlDjofWqNGaX2i1PbtOXOM3BADQL169rt3xccrlbzLWHbtn5/kln/T/HJv5obv4Yr7O9f9HymKeapVuIZcT9epnnGRtOXoVA1KqUWABoZinqL6EbjPzlNUnYF5mKeozmAeE9+SujOyneNvy0p1lkhJrqfryLV0LbmeriPX0rXkerpOVq+lhyuDccAozLg254GFmLFtwpVS5ZRSUUqpcgDWvjfvAWuBE9ZlfA7HKoQQQog8KkfHwdFaXwZ62tl+EghKtW0KMCVnIhNCCCFEfpLTNTjZbaa7A8hn5Hq6jlxL15Lr6TpyLV1LrqfrZOla5mgfHCGEEEKInJDfanCEEEIIISTBEUIIIUT+IwmOEEIIIfKdPJXgKKUKK6W+U0rdVEqdUEr1S6fsC0qps0qpa0qpOUop35yMNS9w9HoqpQYppRKsj/LbljY5G23uppQarZTappSKUUrNy6Cs3JvpcPRayn3pGKWUr1JqtvX/+A2l1E6lVJd0ysv9mQZnrqXcnxlTSn2llDqjlLqulDqklBqaTlmn78s8leAAUzFzUoUC/YHpSqnaqQsppToBrwD3AxWASsDEnAszz3Doelr9qbUOSrasy6kg84hI4E1gTnqF5N50iEPX0kruy4x5AaeA1kAIMA74RilVIXVBuT8z5PC1tJL7M31vAxW01sFAd+BNpdQdI45n9r7MMwmOUioQ6A2M01pHaa1/B5YDj9spPhCYrbUO11pfASYBg3Is2DzAyespMqC1Xqa1/h5IdzoR5N7MkBPXUjhAa31Taz1Ba31ca23RWq8EjgH2pq6Q+zMdTl5LkQHrfRZje2tdKtspmqn7Ms8kOEA1IEFrfSjZtt2AvRqH2tbPkpcLVUoVycb48hpnridAA6XURWs14jilVI4OEpmPyL3pWnJfOkkpFYr5/29vHkC5P52QwbUEuT8zpJSappS6BRzATM30o51imbov81KCEwRcS7XtGlDAgbK2dXtl71bOXM8NQB2gOKbWpy/wf9kaXf4l96bryH3pJKWUN7AAmK+1PmCniNyfDnLgWsr96QCt9SjM/dUSWAbE2CmWqfsyLyU4UUBwqm3BwA0HytrW7ZW9Wzl8PbXWR7XWx6xVsnuA/wB9ciDG/EjuTReR+9I5SikP4EtMv7vRaRST+9MBjlxLuT8dp7VOsHaTKAOMtFMkU/dlXkpwDgFeSqmqybbVw37VYLj1s+TlzmmtpU0/iTPXMzUNqGyJKv+TezP7yH2ZBqWUAmZjHijorbWOS6Oo3J8ZcOJapib3Z8a8sN8HJ1P3ZZ5JcLTWNzHVV/9RSgUqpZoDPTBZdGpfAEOUUrWUUoWA14F5ORZsHuDM9VRKdbG2NaOUqoF5cuCHnIw3t1NKeSml/ABPwFMp5ZdGe7vcmxlw9FrKfemU6UBNoJvWOjqdcnJ/Zsyhayn3Z/qUUsWVUo8ppYKUUp7WJ6X6Ar/ZKZ65+1JrnWcWoDDwPXATOAn0s24vh6nCKpes7IvAOeA6MBfwdXf8uW1x9HoC71uv5U3gKKaq1dvd8eemBZhA0lMAtmWC3JvZdy3lvnT4epa3XsPb1utnW/rL/Zl911LuzwyvZTFgPXDVeq/tAYZZP3PJfSmTbQohhBAi38kzTVRCCCGEEI6SBEcIIYQQ+Y4kOEIIIYTIdyTBEUIIIUS+IwmOEEIIIfIdSXCEEEIIke9IgiOEcBml1HGl1JicPJ5SKkopNSiDMvOUUiszGcMEpdSczOzrxDlGK6WWZ+c5hLjbSIIjRD5j/WWurUucUuqoUup9pVSgg/tXsO7bOLtjdUATYJqjhV0du1KqOGaAsTddcbx0zAIaK6VaZvN5hLhrSIIjRP70K1ASqIQZ1nwUZmTVPEVrfUFrfcuNIQwFtmitj2bnSbTWMcDXwLPZeR4h7iaS4AiRP8Vorc9qrU9prb8GFgA9wUwWqJT6t1LqiFIqWim1Ryk1INm+x6yvW621Ieus+zVRSq1WSl1USl1XSv2ulGrmaEDWOWfilFJNk207rZTan+x9B6XUTaWUt/V9iiYqpVQVpdQ6pdRtpdRBpVTXVKexG3uy/Z9TSkUopa4opeYqpQIyCLsfkKLpyHr9XlJK/aOUirF+h7etn9lqkB5TSq23Xt+dSqm6Sqk6SqlN1u/3u1KqYqpzLQe6OxCTEMIBkuAIcXeIBryt628CQ4CngVrA28AMpdSD1s/vtb52xtQC9bK+L4CZjLWltcwu4EelVFFHAtBaRwE7gLYAysxkHwJUUEqVtBZrA2zSdmZoVkp5AN9hfm41AwZj5qjyTVYsrdixxl0HaA88CjwEPJdWvEqpwpjrsy3VR5MxEye+DdQGHgZOpSozEXgXaICZa+dr4FNgrDVGP+CTVPtsw8ym7HDSKIRIm73ZjoUQ+YhS6l5MTcQaaz+cF4GOWuuN1iLHrGWeBsKAC9btl7TWZ23H0VqnmOVXKfUM0BuTTHzlYDjrMAnOO5hk5ncgwLq+0Pr6Yxr7tsckHBW11ietMTwPbExWxm7sVteBkVrreGC/Uupb4H5MomJPOUABZ2wblFJBwAvA81prW8fjw8CfqfadorX+0brPB8AKoLfWeq112/+A/yXfQWt9Syl1DaiQRjxCCCdIDY4Q+VNn69NFtzG/fDcAz2ASBD9glfXzKKVUFDASqJzeAZVSxZVSM5RSh6y/iG8AxTGJgKPWAc2tTVBtgLXWbW2sTTNNrO/tqQlE2JIbq78Ai4Pn3mdNbmwiMfGnxd/6ejvZtlqYGqM1GZzr72Tr56yve1JtC7TTHBWd7LxCiCyQGhwh8qcNwHAgDoi0Nfkk6/fRDTiZap87moVSmQ+EYmowjgMxmF/0Pk7EtRGTIDQBWgMfAUHADKC5NYYtaeyrnDiPPam/nyb9P/IuWl8LkVSL42gMyc+l09mW+vyFSaqFEkJkgSQ4QuRPt7TWh+1s34dJTMqnbnJKJtb66plqewvgWa11GIBSKhTTz8VhWusopdQOTPJVANMnxxtTC9SfNPrfJIu9tFKqrNba1uflXlImCWnFnhlHMM1atazntsUQg2na+scF50iklKqMqV3b4crjCnG3kiYqIe4iWusbmMfF31dKDbY+lVRfKTVCKTXcWuw8pqmkk1IqVCkVYt1+CBiglKqllGoCLCIpoXDGOmAAsFFrnaC1vo1pahpA2s1TYB59PwB8YY25GfAhkLzZKa3Ynaa1tljP2SLZthvAx8DbSqknlVKVlVL3KqVGZvY8ybQEjmqtXZo4CXG3kgRHiLvPOMzTR2OAcOAXTGfhYwDWfirPYsaAiQR+sO43GNOctB2T3MzBNFU5ay2mhmVdBttSsCYcD2F+bv0FfIF5IiwmWZm0Ys+smcCjSqnkNUKvYp6QGgfsB5YCZbJ4HoC+mAH/hBAuoLTWGZcSQoi7lFLqT2Ca1vrLbDxHHUx/pmpa62vZdR4h7iZSgyOEEOl7iuz/WVkKeEKSGyFcR2pwhBBCCJHvSA2OEEIIIfIdSXCEEEIIke9IgiOEEEKIfEcSHCGEEELkO5LgCCGEECLfkQRHCCGEEPnO/wPcdIZU2d1JmAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "decision_boundary = X_new[y_proba[:, 1] >= 0.5][0]\n",
    "\n",
    "plt.figure(figsize=(8, 3))\n",
    "plt.plot(X[y==0], y[y==0], \"bs\")\n",
    "plt.plot(X[y==1], y[y==1], \"g^\")\n",
    "plt.plot([decision_boundary, decision_boundary], [-1, 2], \"k:\", linewidth=2)\n",
    "plt.plot(X_new, y_proba[:, 1], \"g-\", linewidth=2, label=\"Iris virginica\")\n",
    "plt.plot(X_new, y_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris virginica\")\n",
    "plt.text(decision_boundary+0.02, 0.15, \"Decision  boundary\", fontsize=14, color=\"k\", ha=\"center\")\n",
    "plt.arrow(decision_boundary, 0.08, -0.3, 0, head_width=0.05, head_length=0.1, fc='b', ec='b')\n",
    "plt.arrow(decision_boundary, 0.92, 0.3, 0, head_width=0.05, head_length=0.1, fc='g', ec='g')\n",
    "plt.xlabel(\"Petal width (cm)\", fontsize=14)\n",
    "plt.ylabel(\"Probability\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 3, -0.02, 1.02])\n",
    "save_fig(\"logistic_regression_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.66066066])"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "decision_boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.predict([[1.7], [1.5]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Softmax Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure logistic_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = (iris[\"target\"] == 2).astype(np.int)\n",
    "\n",
    "log_reg = LogisticRegression(solver=\"lbfgs\", C=10**10, random_state=42)\n",
    "log_reg.fit(X, y)\n",
    "\n",
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(2.9, 7, 500).reshape(-1, 1),\n",
    "        np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "y_proba = log_reg.predict_proba(X_new)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n",
    "\n",
    "zz = y_proba[:, 1].reshape(x0.shape)\n",
    "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n",
    "\n",
    "\n",
    "left_right = np.array([2.9, 7])\n",
    "boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n",
    "\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n",
    "plt.text(3.5, 1.5, \"Not Iris virginica\", fontsize=14, color=\"b\", ha=\"center\")\n",
    "plt.text(6.5, 2.3, \"Iris virginica\", fontsize=14, color=\"g\", ha=\"center\")\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.axis([2.9, 7, 0.8, 2.7])\n",
    "save_fig(\"logistic_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=10, multi_class='multinomial', random_state=42)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]\n",
    "\n",
    "softmax_reg = LogisticRegression(multi_class=\"multinomial\",solver=\"lbfgs\", C=10, random_state=42)\n",
    "softmax_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure softmax_regression_contour_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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5mP8vC/MrWeiH+mGcEILuEtc+DPh3ttJrXhGdXywh5W13Uud6cHCxG/5dLSROLqPF9aqdtUKhUJwpnJZ2UFJKG/CPEOJW4B7greOGlABHl32qvy9uhvAUCoWLVORZsBTb8IlpgKGy3UbbD54gfNW3ZPUcRsqIJ7B4B5zyMKnTUx7aivLQVuR2ubxmLq+DyfgnryJg53JC56whYsZabJ4GCq6II+/qRPKvisfme3I5iNAE+oG+6Af6Yk+vxFwlvyj7rgCtnRvGe0Mw3ByA8Kq7lfbxuIfZ6fTfUto9Vsq+T9xJftODVaN92fSEFwkTyoi7sxxToPqsr1AoFKeT090vVY9Dg3w824HOwBdVP3cGso+XVygUioYjGyEXKz3guBDkFVV//XHMkpmEr/qW9Ksmkj5kEg3SHWg6Slq0o6RFO/ZfNgbNXIF/8iqCtvxO0O+/E/jtQuxGHQWXx5I7oi1HhiVg9z65UY4WY8LtpShMz0Rg+eII5pmHqbg3g4onDmIcFYjxnhC0WOfNdvTuEDe2nNjR5WT9YmTXNA+2PO3N9he9iLm9nISJZfgkKp2yQqFQnA6aLUEWQoQA/YHvgXLgMuBmYGQtwz8A5gshPgYygaeA+c0TqUJx/iA0GqVVclmWI0H2iKifG6P3vm20WjqLzF7XNDw5rgW70Y28jpeS1/FSkm9+Dp+9m4kwv07g1zsJWJKCzU1P/pDW5NzcgYKBcUhj3RVh4a5hvCMIw+2B2FaVYp51GPPMw5jfOox+kC/GiSHoBng7Lb8QGoQPNBM+0EzBNh3Jb3mS9r47e+Z4EDG4ksT7Swm5ROmUFQqFojlpzgqyxCGnmI3DXm4fcL+UcqEQIhrYAbSTUmZIKX8UQkwF/sCxme9r4NlmjFWhOC/QNLA3QoJcftgCgHtQ/ZpjxH/1MmbvAFJueKrRk+MT0DSKYrtSxIfwuB2f9E1ElrxC0Fc7CfpqJ5ZAd3JvaMfh2ztR2i28zniO3tRn/z8z5ndysbybQ9ngFLQ2VfKLWwMQns7LL/w62Oj5ThGd/1dCyhxHkvzHFQH4dXbolKNvVDplhUKhaA6azQdZSpkjpbxESuknpfSRUnaUUs6teixDSuklpcw4avzrUsrQqrGjpZS1beZTKBQNoLEqyBX5jgTZFOB6gly5fj/+KWvIuOIurB7OOU40GppGUVw3dnb+lHV7J7Pzuxso7B9D6LxNdO79Pl26ziXi9VUYsktOPk2EEbfnIvDa0xG391qBh0bFpAyKY7ZS8egB7Htde/lyC7XT8ZlShu7J4YLZRUiLYPVYXxa3DmL7yx5U5qlyskKhUDQlqtW0QnEeo+lAStFgHbK50NEqzujr+kWpkvfXYDO6c6jv9Q0LooGUfziGzKzn2TLgO9buv5/UWYOweRtp9dhvJMVMJ/H6r/D7YQ/Y6v5EIdw0jLcF4rmyDR7LEtFf5oP5rWxK2myj7IZUrH8XI1042Xp3iBtTzpUb87hkcT5+HaxsfcabRbHBrJvoTdFu56vTCoVCoXCe071JT6FQnEa0qvzKbgNdA14NLCU29J46NJ1rlU1ps1P67Va8r07A5u5V/wAamdJvxlOqwb7R4P/Oa4Qs2EzIh1sIXJhMZZQ3h0d1IXt0F8wtaq94CyHQ9/FC38cL+34z5rcPY5lX5X7RxR3jxFAMN/ojTM7VKIQ4Vqe8e7onaQvc2TPXnYhBZhLvKyXkUqVTVigUisZCVZAVivOY6qTYZm3YPNZSGwZP119OzJsPYc8pxeOqdowZs/DUB5wG8lc+xL6XB7AufTK7PhtOWbtgol74m6TWM2hzzef4L0k5aVVZa2HE7cUovNI64TYrGiolFXfupSR+KxVTDmHPtrgUj18HGz3mFDFsTy7tnyglb62BPwYG8HPPANI/csNmbuhvrFAoFApVQVYozmOOriA3BGu5Db2H65f7K5enA+B2SW1uj/VD2K145m7HPX83xrLD6CylSE2HzeCFxSOYCu8WlPvGYXU/tcdyNRXz7gAc9jtHvl+AKb2A0HkbCZm/mYClX1AZ7UPW2K4cHt0FS1jtlXDhoWG8MxjD2CBsvxVjnp6N+flMzFOzMNwYgHFSCLouHk7H5BZqp+OzpbR7tJS9VX7Kq8f4svlJ5aesUCgUDUUlyArFeUxjVZBtFXZ0RtcryJXrD6CL8EEf6duwAKTEf9+vRG6ZTcC+X9CbT91TyOwRQklQJ4rCulMU3puCyL5Y3QNPeVzFvDuoAApjYH/aPAIW7SZ07gZaPvsnLf73N0euSSTr7iSKLoqu1QFDCIH+Mh/0l/lgS67APPMwlg/ysHyYh+4SL4yTQ9EP9kU4KVfRuTl0yrGjy8n6+Sg/5ZeO8lNOUH7KCoVC4QoqQVYozmP0BkeF0ebaVf4TsFXa0eqRIJu3ZWLsFNGgtd0K0mjz690E7PsFs0cIWW1voTDyYkoD21HpGYbd4AnShs5cgrE8B7eifbgX7MEzbwdehzcRve5VNLvjE0JJUEeORA/gSKuBFERdgt1w8s6A5R+OIW/MAvKGt8Vtdx5hczcQ/MEWgr7aSVm7YLLu7sbhWzrW2YREl+iG+1vRuP03AvP7uZhnHqZ8eCoizoRpYgiGOwKd7tJ3jE55q57ktzxIm+fOntkeRA6pIPGBMoIvVDplhUKhcAbhyo7qM52kpHi5atVrpzsMheKsYekcjdmTDCzIqMQ/rAHzXLOJskwzI1b3cPoYabeT4f8U3uN6EfDKMADmzbvapXV9MlfT6Zur0OwW0vo+z8FO45B615qVaJZyvLPX4XfgL/z3L8P30D/orBXY9O4cib6M3Lhh5MYPw+IRUuccbmMW/DtfmYWgL7YTNns9XhuysHobybmtE1l3J1HeJuiksUirxPptPua3DmNbXQq+OoxjgjBOCEZr6XoTlvIsjT1z3EmZ7YE5T8O/i4XE+8uIvr4CrX6W1QqFQnFWM8o4ar2UsvupxqkEWaE4j/l5nsaMuw28l1pJcIv6z7NkyEYq861ct/wCp4+xZhZxoOX/CJh2DT739AVcS5A98naR9GkvrG6BbBr+E+X+8S7HXRuapRy/A38SmLaEoLTFuBftQwqNgqiLOdx6BDkJwzF71v1poiZZlhKvtYcIe3s9QV/uQDPbKLgshsx7upM/OB50J6+4W9eUYp6WjfWbfJCgv8YP4/2h6Hu57vZhLYO9n7ize5oHRcl63CNtJNxbRtzYcoz+5857gEKhUJwKZxNkJbFQKM5jGkuDLO2OpiOuYDtQAIC+hb/L6wm7lfZLRyI1Ixtu+INKn2iX56gLu8GdIzFXciTmSlL6v4VXzhaCU74hOOUrEn+fSMIfk8lvcSnZbUaS03o4Vje/Y46v3tAHwJgF7OkRyb7/G0DIexsJm7uBtsO/pKKVL1l3dyd7dGds/rXLOPQ9PNF/HOuwiZt1GPN7uVi/KUC7wAPTfaHor/NH6J3TS+g9IP7OcuLGlJP5o5HktzzY/IQ321/wJOaOChInl+EVq3TKCoVCUY2yeVMozmNqEmRLw4Sp0i5Bc20OW2aRI4YI17vnRWyejffhjSRf9najJscnIAQlIZ1J7/tf1ozazqpR29nb8yncijJo+/Od9J0dRodFIwjaswhRi5C7Olm2hHhy8PELWb97IsmfXkdlC19aPfYb3Vu9ReyEpXhsO1xnCFoLI24vReGd1hG3aS0g30b5remUJG6l8rUsZIHzn26EBhGDzfT7sYCBa/KIuq6S1LnuLGkXyD83+JKz3NDgpjEKhUJxLqAqyArFeYze6Phqbah3rqxHBTmnFABdkKdLxwmbhVZrXiI/6hJyWl/n2qINpCywHel9/0t6n+fwzl5H2I6PCN31KSEpX2N2Dyar7S1kdhhNaXCnmmOOrii7VW3oyxveFo/N2YTPWkvwR1sJe3cjBf1akXlvd/Kval2r/EJ46TDeE4JhfDDWJYWYpx+m8vGDVD6fieGOQEwTQ9Di3Zz+Xfy7WOn1XhGd/1fC7lkepL7rzoHv3AjobiHxvlJaDK9EU+8QCoXiPEVVkBWK8xh91UYtawNdLOqD/UgZAFqgawlyYNr3mEoOkdH9oVpt1JoFISgOu4CU/tNYPv4gm69ZTEHUxURtmknPDzrT/aPuRG56G31FwTGHVcy7o+ZW1jmU1DlDWJ8+iX3P98N9zxHajviKbu3fJnzaanSFFbUvrQkMQ/3w/DkBzzVtMVzjh2VuLiXtt1M2fA/Wv1xrZ+0eYafz8yUMS8sh6a0iLAWClbf58X2bIHa97oG5UNleKBSK8w+VICsU5zG6qgS5oRrk+mAvrAC9hvBwzU4hNPlzzB4hHIkZ1ESRuYbUGciLG8K2YV/xz92Z7O43DWG3kPjbBPrOCaftD3fge3A5x2sXqhPlkoX3cPCRPqxPvpfkT67DHO5NzMO/0j1mOjH3/Yjb7rw619Z18cD9/Ri89nTE+GgYthUllF22m9Leu7B8egRpcT5R1ntA67vLGbwtj4u+LsCzlY1Nj3mzKDaIjQ97UZKu3i4UCsX5g3rFUyjOY/RGRwLVYImFcGzUcwV7cQWajxvChSqwsFsJ2PsjubFDkWfg9X+reyAHuk1m7W2bWHvLWrLa3UHwnm9J+uxCeizoQNSGaegr8k84rmLeHaDXyBvRlm1/3M7mVWPIuyaR0Pc20a3DbNpc8zm+v6adkGRXo4UbcJsSiVdqJ9xmRkOJjfI70ilJ2Erl1CzkEdd0ypFDKxnwaz5XrM4jYnAlu2d6sKRtEMtv9iV3tfKHUygU5z4qQVYozmMaS2IhNAF213Z3yVKzy9Vjr8MbMVQWcqTl5S4d1+wIQXFYd5Ivn83y8YfYecW72AxeJPxxP33nRND2x1H4HFp1TMJ7tPyitFs4e+YNY33qRDKevgivdZm0H/wpXbrOJeS9jWjltf/BhIeG8a5gPLe0x31hPFqiG5VPHaQ4divl92VgS6ldtlEXAV2t9PmwiKG7c0l8oIysX438elEAv1zkz/5vTNhPw5UHhUKhaA5UgqxQnMc01iY9odWjglxuQbgbXTrGJ3M1AIURfVxb7DRiM3qR2XEs629ZzZpbN5DZfhTBu7+m+6e9ueCjJCK2zEWzlB5zTHWibAn14sDTF7M+dSIp7w7FbtSIv2cpSbHTiX76DwyHam+pLTSBYZAvnj8m4LmuLYYR/ljezaW0w3bKrtuD9W/XdMoeUXa6vFTCsPRcur1RREWOxvKb/FjSLojdM9yxFCudskKhOLdQCbJCcR7zb4LcwARHEw6rNxeQFVaEm2syCe+czVjcAqj0jnLpOKfisRVgL12GLf9dbDkvYz38HLbDU7DlvoGt4CPspcuQloMuJZbHUxLald2Xvc3yuw+RPGAWwm6lzS/j6DsnktZ/3I/HkeRjxlcnytKkJ+f2TmxZPZZtv95KUd8WRE5dQVL8DFrf/h1e6w7Vuaaukwfu77bCK7UjxsfDsa0soWzAbkp77cL8cR7S7PwnG4OXJOHecq7anseFXxTgHmFjw4M+LIoJYuOjXpQdUG8pCoXi3ODME/EpFIpmQ1/1CtBQiYWmCaSrfSYsNoRR59IhHkd2URrYvtHcK6S0YC/6Cnv+XGTpX4ATv4Tmi3DrgnDvjubeC+HRF2EId2ldm9Gbg13u4WDnu/E9tILITTOJ3DSLFhumcST6Mg50nUhu7BDQHOenYt4djg59QlB0cUuKLm6JKS2f8LfXETJvE8GfbaeoTxSZk3qQd3Ui6E9MVLUwA27PRWB6JAzLJ3mYpx2mYvReKp88iHFCCMa7ghD+zr0laDqIuqaSqGsqyVujJ3maJ7vf8mD3Wx60GF5JmwdKCUhS+guFQnH2ohJkheI8prqCbKls2DxCL7BbXawgW2wIg2sJsntBKnmtrnTpmLqwl2/EdvBWZOUOMLZGC3oUzfMShDER9CEIzR0prWAvBmsO0rIPaU5BVmxFVmzEfmQGdlnV2t7YBs3rMjSvgQjPfgjNSes6ISiM7EthZF9SLn2DyK1zidg8h04Lr6HcpyUHO99DZoexWDyCTvBTroz1Z+8rl7P/6YsJmb+Z8FlrSbz5Gypa+pJ57wUcHt0Zm++JvsjCQ8N4ZzCGMUFYfyrC/FY2lU8dpPLFKj/lSa75KQf2sNLn40JK9mqkzPIgbZ47GV+4EXyhmcT7yogYUlmd5ysUCsVZg0qQFYrzGIOpcVwsNB1Im4vSA6u91kpnXQibGWNpFhU+LV2M7kTsRd9gPXAT6ILQt/gG4X01opZOJ0LoQecPOn+EKQH4d3OgtJuRFZuQZX9hL/0Ne/572I/MAGFCePZH874GzXsYwhDmVEwWz1D29nqKfT0eI2jPQqI2zSD+78eIWfEs2W1GcqDrJEpCuwInNh/JnNyDzHu7E7B4N+HT1xLzyK9ET/mL7FGdybz3AirjTmznXa1TNgzyxbalDPNbh7G8l4tldg76Ib4Y7w9Fd6GX0y4jXq3sdJ1aQoenSkmd587umR78c70fXvFWEiaWEXtHOXrXLK8VCoXitKEEYwrFeUxj+SDXq4JssyNq6RhXF8bSLASSSq9IV8M7BnvpMqwHbkK4dccQtxXN59pak+NTITQjmkcPdEH/wdDyBwxt8tG3/AUtYAKyMhlb5ngsuyOwpF+ELW860lK3TvhopKYnJ2E4G2/4g9V3bCWzw2hCkz+nx0fd6PbZRQQnf4k4yj6iJlnWaRy5pg3bf7vNYRM3LIGw2evp1m4WiSO+xPufjDpt4mp0yns6Ynysyk95wG5K+7jup2zwkbS5v4whO3Pp83EBpgA7G+73YVFcMJuf8qL8kHrbUSgUZz7qlUqhOI+p2aTXUA2yXnN5kx52CZrzWmJjWTYAZs9Q19Y5CmkrwHpgJBhi0bdcitAH1nuu4xGaCc3rMvRhr2NovQd93BZ0wf8FWyG2rMlYdkdhSb8U25F3kLYTvZBrozSog2NT3/iDpFz6OqaSQ3T8/gZ6z42h5eoXMZTlAsdaxAEOm7j5V7N+z0QOPtwHn3/207H/h3TqPY+gT7YhzLVrrbUwA27/jcQrrcpPubjKTzlxK5WvZiHznf8kpekh+vpKLv8nn8v+PELIxWZ2verB4tZBrBrtQ/4mdQFToVCcuTRbgiyEMAkh3hNC7BNCFAshNgoham2FJYQYJYSwCSFKjrpd2lyxKhTnC4YaDXLDNr0JvcDuQpXx3wOdH2ood3SUs7jVP6m15bwE1iz0UR8jdH71nudUCCHQ3DqiC3kaQ/wWDPE70AU/i7RmOSrLyWFYMq7DXvQd0n5qfYvVzY/9SQ+wcsxuNl+ziLKANsT98yR95ragzU9j8czZUjP26GTZEuFNxvP9WJ82idSZg9BKLCSMWki3hBlE/t9y9EfKa4/f/Sg/5e/i0eLdqHzC4adc8UAG9lTXROtBvS1c+EUhV+3II25cOQe+M/FTj0B+H+jHwSVGly0CFYqmoKCkgBc/fJGCkoIzZr3mjknxL81ZQdYD+4FLAF/gaeALIUSrOsavlFJ6HXVb1jxhKhTnDwaT46u1gZv0NIPAbmnaLMdQ1YHO6naintYZpDUP+5EZaL63oLknNWZop0SY2qILeRZD/E70sevQ/Ccgy1dg3X8tlt2RWDPvw16x+dQTaTry4oay6fpfWH3HNrLa3UHors/o+UFnun7Rj6CU78D+b3W4uqJs9zCQfVc3Nm0Zz46FN1LeNpiWTy8jKXY6sZN+qLOdtdAEhsG+eP6cgOeathiu8cP8Ti4l7bZRdn0q1hUlLtneecXaSHqjmGHpuXR+sZji3Xr+vtafpZ0C2fOuO9ba83WFollY+M9CUg6ksOifRWfMes0dk+Jfmi1BllKWSimfk1LulVLapZTfA+lA875TKRSKGmpcLBq6Sa8eGmRX0ZmLALCafOt1vL3wI5BlaEGPNGZYLiGEQHNPQh/+BoaEA+ijv0d4Xoo9fzbW1C5YUpOwHZmFtBWccq7SoPaOTn3j9rPn4qm4F6TRadG19J7XmhbrXkdXWQgcJ7/QBAWD4tnxw0g2rb+L3OvbEvL+Zkc762u/wGfZ3rp1yl08cH8/Bq+UDhgfDsP6VzFllyZT2ncXli+OIF34+xv9JG3/U8bQ3bn0WlCI3kOyboIPi+OC2fqcJxXZSv2naF4KSgr4Z8s/SCn5e8vfTV6xdWa95o5JcSyn7VVICBEKJADb6xjSVQiRK4TYLYR4WghRq2BNCDFOCLFOCLEuN7eoyeJVKM5FNB0IIRvuYmEQ2M0uJsjCtfbUOksJADaDl2vrVGEv/ALh1gXNrWO9jm9shNCjeV+FocWXGBIy0YVNB2zYMu/FkhyO9cDt2Ev/PmWF1uoeQMYFD7PyzlS2Dv2KSq8oWv/5EH3nRNH698m456fUjD3a/aKsYwipc4eyPnUi+5+8EO/VB+lwxcd06vEewR9uqVunHGHE7flIvNM64jY9GgpslN+aTkmbbVS+kY0sdN4QWzNAq5sruGL1Efr/eoSgXma2v+TJorggVo/zoXC78odTNA8L/1mIvUrrY5f2Jq/YOrNec8ekOJbTkiALIQzAx8ACKeWuWob8BXQAQoDhwM3Aw7XNJaV8R0rZXUrZPSjIp6lCVijOSYRwVJEbniBrrleQBeDCIbqqdsx2g4dr6wDSegRZvhLhfbXLxzYHQh+ALnAihrhNDgmG3yjsxd9h3XsxltT22PLeRFqPnHSOaveLDTf9xZpb15PT+loiN8+m17xEOn47DP+M30HKEzb0WUK92P/sJaxPncie2YPRzDZaj11MUusZRL70D/q8stpj9tRhHB+M57b2uH8Vh9bKSOWjByiO3ULFf/Zj3+u8bkcICLnYwkXfFDJ4ax6xo8vJ+NyNH7oGsewqP7J+NdZV2FYoGkx1pdZmc3y4s9lsTVqxdWa95o5JcSLNniALh5/Sh4AZmFjbGCllmpQyvUqKsRWYAoxoxjAVivMGvbGRJBYutCx2HORae2rNWoFd6JCa6+4HsuwvQKJ5Xubysc2N5p6EPuJtDImZ6CLmITQfbFkPOLTKB0dhL1t1yqpySWg3dg76gBV37WNvr6fwzVxF1y8H0OODzoRvnYdmrQA4JlG2uxs4PKYrmzaNY8f3N1HaMYSWz/7p0ClP/AG35JPolIf54flrIp6r2mAY4od51mFK2myj7OY0rKtLXPr9fRJsdJ9ezLC0HDpOKaZgq55lg/35sVsAqe+7YatwaTqF4pQcXamtpikrts6s19wxKU6kWRNk4XCcfw8IBYZLKZ01l5K4tN9doVA4i8EEVnPD/r10RoeLhSsbtoTmmsRCs5mROlN9wsNevhrQI9y71+v404HQPNH5j8YQuwp93CZHVbnoa6zpvbGmda2yizt58mn2Cie97xRWjMtg58B5ALT9eSx93okmZvkzGEuzgGMTZYSg4Io4dn5/M5s23EXuTe0JWbCZbh1n0+aaz/H5Y2/dOuVunrgviMFrd0eMD4Ri/a2IsouSKb14F5av811qJmMKlLR/rIyhKbn0mFuI0GDteF8Wtw5i2wueVOSotwRF45B6MLWmUluNzWZjz8E9p2295o5JcSLClTe0Bi8mxGygC3CZlLLOV/Yq+7cNUspsIUQb4CvgSynlf082f1JSvFy16rXGDFmhOOcZ1cpI0kA7k+bUv1vI+hfSWfvfNMaV9UNzsjte1qB3kKVmwv/690LSvHl1SyBa/z6ZsB0f8vdE5zyEj8aybxBYMzHEbXL52DMJaSvGXvgJ9iOzkJVbQPNB87sDXcC9CFOiExNI/Pf/QdT6NwlOW4xdM5DddiT7uz1ASUjnY4a6jVlQ873hcClhs9cTNmc9hpwySjqHkjm5B7k3tkca69YJyxIb5vl5mGdkI9PMiBgjxntDMI4OQni7pi+WErJ/N5I8zYPMH03o3CStbisncVIZPm2c1z0r6k9BSQGzvp3FhGsn4Ofld7rDcYl92ft4+aOXefzWx4kOjT7d4ShOI6OMo9ZLKU9ZLWlOH+SWwHgcCXLWUf7Gtwghoqu+r37WDgC2CCFKgaXAN8CLzRWrQnE+YTCBpaE2b0ZHNc/mykY9nUBanZdlCLu1XvIKAFm5C2FqV69jzySEzhtdwHj0cZvQx/yD5j0Ue/5sLHvaYNl7mcNXWZ4kWRSC/Oj+bL12EStHJ3Oo0zhCkr+kx4dd6PpFf4L2LKLalPgYnXKIJ/ufuZh1qZNO1Cm/vLxunbKXDtPEELy2d8D981i0cAOV/zng8FN+7AD2DOe1PUJA2AAzlywqYNCmXFqOLCf9A3eWdgrir2v8yP7DoHTKTczZbDk2Z+EcyivLmbNwzukORXGW0Jw2b/uklEJK6Xacv/HHUsqMqu8zqsb+R0oZKqX0lFLGSimfcUGOoVAoXEBvaAQXC6PjpcQVHbLQ68DmwnhpQwrXXQ2ktIAlAwxxLh97piKEQPPoiz7qIwwJ+9GFvICsTHb4KqfEYst5GWnNPekc5QEJ7B4wg+XjD1TZxO2h08Kr6TUvkciNM9CZHRf5jk6UpZv+WJ1yhxBaPuOEn7JOYLjWH89lbfBc3gb95T6Yp2VTkriVstvSsK0vden3921no8fsYoal5tD+qRLy1hr4Y2AAP/cMIP0jN2wNfD4rTuRsthzbl72PQ7mOVu8Hcw+SkZ1xmiNSnA0os0mF4jynMSrIuqoKsivd9IRec62CLO0g6vGSZTkE2BHGlq4fexYg9KHogp/AkJCOvsXXCGMctsOPY9kdhfXgGOzlG096vNXN32ETNzaVbVd9hsUtgMTfJ9HnnRbE/fkIpqL9wHF+ytU65SVVOuUb2xPy/ma6dqzyU/5zX9065Qs88fgkFq9dHTBODsW6tJDS3rso7Z+MZVGBSzpltxBJx2dKGZaawwVzCrFVCFaP8eX7hCB2TPWg8ojSKTcWZ7Pl2PFVY1VFVjiDSpAVivOc/3xoZeyr9dcfg8PmDcDmipOFTgMXEmSkRNYjQZbWTACEPsLlY88mhNCj+VyHodXv6OO2Ojb1FX6ONa0blvSLsBV+zskuxEmdgcNtbmT9LatZd/MKjrS8nOj1r9H73RjaLRmJd+aamrFHJ8tlHUJIfWcI61MncuCJKj/lyz+iU8/3CPp4a91+yi1NuP1fFN7pnTC9EoV9v5nyEamUdtyO+e3DyFLndcU6N4gbXcGgzXlcsjgfn7ZWtjzlzaLYYNbf703xHuWn3BDOZsuxo6vH1agqssIZVIKsUJznRLeThMU0bI5qDbIrzUKEQYe0NMPmKuthx1d9SNOvdYaguXVAHzEbQ+JBdKGvIS2HsB24CcvuWGw5LyKtOSc9viiiN9uHfsHKsakc6HYfQWlLuOCTnnT79EKCd39dazvrY/yU3x6MVmEjYfQiuiXOJHLqCnT5tfeRFj46TPeF4rWzA+6fxCIC9FTct9+hU37yIPZDrumUwwea6fdDAVeuyyN6RAWpc91Z0j6Qv4f7krNc6ZTrw9lsOVZXtVhVkRWnQiXICoWiwegMrmuQ0WtgbfoEWdocWlyhC2rytc40hM4PXdCDGFrvRh+9CGFqg+3wk1h2t8B6cCz2is0nPb7CtxV7Ln2N5eMPsLvfm5hKD9Fx8Qh6vxdP1Po30VU6upee4Kc8tkqnvPBGytsE0fKpP+geM52Y+3/CbU/tDU+EXmAY4Y/H34l4LEtEf4k35teyKGm9jfLR6dg21b4RsC78Olnp+W4RQ/fk0u7RUnKWG/mtXwC/9A1g3+cm7A27aHJe4YrlWEFJAS9++OIpq8vOjHN2rpORU1D7h8HDBYebZL3GnqsxYzqXaYrzpBJkhULRYOrjYiEMOpc0yADCldZ71dgKHF91fq4fe44ghA7NeyiGVr9giNuO5jcae+GnWFO7YEnvd0r3C5vRmwPd7mPlmJSqdtaRJCx7gL7vtCB+2UO4Fe0DjvNT1gQFg+LZ8cNINq27k7wRbQmdu4Gu7d8mccSXeP+TUatOWQiBvo8XHl/E4bWjA8a7g7EsLKC0x05Kr9iNZWmhSw1m3MPtdJri0CknTS/CUihYeZsf3ycGset1D8yFSqd8KqaMncL8J+bTr1s/hBD079af+U/MZ8rYKSeMddbpwplxjeGaMfeRucx/Yv4Jt7mPzG2S9Rp7rrPZOaQ5aYrz5FSCLIRwE0I8KoT4WQixSQix5ehbo0WjUCjOSnTVLhYWFxJeg+aSxEIKrcaCzBWk3VHlRPN2+diGIJHkG9eyy/d/rAwZzC8R8XzfwpeF0UYWRbuxNCqE38LbsyJkEFv8J5Pu9TZ5phVYhWuODq4i3No5OvUlHEAXOhVpSatyv4jHlvsG0lZY98GaztHO+uZ/WHvLGnJjryJqwzR6vxtL+8U34nNoFcAJ7azLOoWy592hrN8zkQOP9sVn+X469v+QTn3eJ+iz7Yg6ngdarAm311rgndYR04uR2PdUUH7NHko778A8NwdZ7vzzQe8JrceXM3hrHhd9XYBnjI1Nj3mzKDaIDf/xomSvqhedDGdcLJx1umjMuRqLxlyvseY6m51DmpOmOk/OviLMAh4D9gLfAV8fd1MoFOcx1TZvrlaQcSWhFprDycJV7CUgPBD1sIirL9luP/BHeBf+DO/BLt9nKdcdwM/cneiS0cQXPURs0WQiyobjZU2gUssmw+t9NgdO4O+wvnzfwoc/wruyxf8+Drl/h1kUNEmMQh+ALuhhDK1T0Ud9iTBEYct+0NHSOnMSsvLkHbuKwy5gx1WfsPLOdDKSHiJg3090/7Q3SZ/0IXj3V4gqDcMxfsrh3uyfcinrUyeROuNKdEWVJNz+Hd0SZxLx2kp0BbX3kRZ+ekz/CcMruSPuC2LAU6Pi3gxK4rZS8dwh7FnOu4AKDSKHVjLg13yuWJVH5JBKUmZ5sKRNEMtv9iV3lcHpuc4nnHGxcNbpojHnaiwac73Gmutsdg5pTprqPDnrun8NcL2U8tdGWfU0UVxsIi8vAItF7WhWOI/BYCMw8Aje3g30QjuHqbF5c8UH2ejaJr36VpCxl4Hm7vpx9cCOmY2B49jvtQAvSwJd8t4houw6jPbAkx4nkZTrMig0bqbAuI4803L2ec0lzectkBr+5gsILb+K8LJh+Fg6IWg8WYAQeoTvCDTfEdjL12PPewt7/hzsR2YivK5CF3g/wrM/QtS+ZqVPC1Ivmcre3k8Tvu19WmyYRsfF11Pu04oD3SZzqMNYbCafmiTZbcwC7B4GssclkX1nN/yXphAxbQ2tHv+dFi/8Q/bozmRO7EFljN+JsRoEhpsD0N/kj+2fEsyvZ2N+KRPzq1kYbg7AODkUXUfn/9YB3az0XlBE5xdK2D3Dg9T33Nn/tRuBvcy0ub+MyKsr0dTbRZ0uFsMuHFbTUc+ZMY09V3P+fs09V3Ofg7OVpjxPzibIZcD+Bq10mikuNpGbG0pkZARubsY6X+wViqORUlJRYebgQQOQrZLkOtBM9bB50+vApQRZV78KsqwA4eb6cS5ix8zq4OvI9lhCQuGTJBY8jQ6TU8cKBB62lniUtyS8fBgANirJN60ix+03Drv/xC7fZ9nl9wzu1mjCy64homwEgZV9EY24lURzT0KLWoC0vIwt/23sR2Zj3XcZwtQRLfB+NN+RCK32c+nQKU/mQJd7CUpdRPT612m97EFiVjzHoY53cqDbZCp8Wv6rUcaRLOcPSSB/SAKeG7MIn7aasLfXEz5zHUeuTuTgAz0p6RV14vkSAv1F3ugv8sa2uwLz9MNYPsjFsiAP3eU+mO4LQXe5j9Ov8x5Rdrq8XEL7p0pJn+9G8nQPlt/kh2eMlcRJZcTcUYHB+/y1vziZi8XtV97u9JjGnquxaMz1Gmuu5j4HZytNeZ6cfWWdCjwoRH1c+s8M8vICiIyMwN3dpJJjhdMIIXB3NxEZGUFeXsDpDueMpUaDXOniJr06PHJrRdPVXLZ3CVkJdSR1jck2/0fI9lhC57y3aVfwvNPJcV3oMBFUeQltC6dwSdZqrjyQSdfc9/A1d2av9xz+CbuYnyKj2Ow/iTzTCmR9NjDWgTCEow+ZgiEhA13Ee4DAdmgslt3RWA8/i7Rk1X2wpiO39bVsuOnvY3TKvd6Nc+iUM1fXDD1aflHaNYw9869mQ8q9HPxPb3yW7aXTxQvoeNF8Ar/aWadnti7BDffp0XildcI0JQL71jLKhuyhtOsOzPNzkRXOf6gyeEkSJpZz1Y48+n5egHuYnQ0P+rAoNohNj3tRduCsfQtsEM64WDjrdNGYc7nCyVwOGtOlo7Fib4pzcCbSUPeJpjxPQtZhCimEOF7EcTFQCOwAjhF8SSmHNTiSRiApKV6uWvVarY+lpESRmBirkmNFvZBSkpycRuvWB053KI2OzQpFuZCxU1BaINAbIKSlJCBc4uOkM1ru5mK+umANV3zekdhrnfMbLnj+Fwqm/EzL8v9D6ByJx7x5V9c5Pn7ZQ0RsmcNfk0ucC6oK6/4bsFdsxdh6p0vHucIR42r+CutNTPEEOufPaLJ1qrGIYrLdl3DQ8wuy3X7ArlXgYW1FVOlIWpTcire1baOuJ6VElv6B7cibyOLvQRjQfG9GC7gfzb3LKY83Fe0nauN0Ira+g6GykIKIPuxPeoCc+Gs5WsPgNmZBzfdaiZmQDzYTPn0t7qn5VLT0JXPiBRwe3QWbT90fPqTZjuXzfMxvZmPfWo4I0WO8OxjD+GC0YNf1xXlr9ex6w5MD35hAQIsRFbR5oIyAbson7mxiwY8LWLZxGf269mtQZbGx5lE4OB3nc5Rx1HopZfdTjTvZx+G8427fAr8DWbU8dlagkmNFfTlXnzslBfD6HXruSjDyfzcZmP+Enhn36Hn0UgOv3GogY7tzv3dNBdkViYXBkRg5q0OWmr5eFWQprQjhrJqsfmz3fwSTLZR2BS816TrVGKQ3UWU30TPnGwYdOEy3XIfmebfPy/wW2Y5lYT1I856BWWucl2chBJpXfwzRizDE70Lzvwt70VdY07pi2dsfe/Fi5EnkL9U65RXj9rO73zRMpZl0XHw9vee1JmrDNHTmYuA4P2UvI1kTLmDjtrvZ9eUIKlv4EPPwryTFTqfVI79izKjdbUMYNYy3BeK5ri0eP7ZGl+RB5ZRMSuK2Uj5hH7ZdtW8ErIvAC6z0/aSQq3blkjCpjENLTfzcK5DfBvhzcLGpXrJ4RfOiXCXOTM7081lngiylHO3srTkDVigUjceM8Xo0Hby93cwn2Wbe2Wnmg/2OW1xXO2+N02NxopFZjQ+yKxILY1Xl0EmZRX0TZLBBEzpYFBg3kOf2F62LHsUgm9dKDhzJcnTp7fQ5/BNXHjhIhyOvYReVbAmYxI9REawJuoFstx+QNE5TFmFKQB8+41+buMoUrBnDsOxJxJY3A2mru8JfrVNeOSaFrcO+ptIzgoQ/7qfvnCji/nwYU5Gj/e8xNnE6jSNXJ7L999vZsmI0+VfGET59DUmJM0m45Vu81h6sPU4h0Pf3wWNhazw3t8NwSyCWD/Mo7bSdsqtTsP5RRF1XUGvDq5WdrlNLGJaWS5f/K6Z0n46/h/uxtEMgKXPcsbrWx0TRjChXiTOTM/18OuuD/LsQwq+W+32EEL83elQKhaJZ2PSbxl2vWwlucez9Jg8Y9ZKNfdsFFicKbrrqTXou2LZVJ8jO6pClZkCTtlqbS5z8QDtN2RMpw/MDNGkiuvSOUw9uYtzsYcQXP0j/zM30O7SJVsX3kOv2OytDB/NzZCt2+j5HmW5fo6zl6NL3MIaENHRRnyF0AdiyJjm69GU9irScZF+3piOn9XUOP+WRq8lrdSUt1r/h8FP+/ma8s9bWDD16U19J9whSPrqW9cn3cui+nvj9lEqnvvPp0O8DAr7bBbY6dMpt3XF/uyVeqR0xPR2ObV0ZZQNTKO2xE/OHeUgXrnwYfSVtHihjyK5c+nxUgMFfsn6SD4tig9n8lBflmeenTvlMpS6XA1erlY01j8LB2XA+nf1PvhQw1nK/G3BRo0WjqDf9+w9h0qSHm2z+0aMnMHTojQ2eZ9myf9Dp/MnNdf7S7/z5n+Djc+JOdkXDCYyQbFmmYa5waJFtVjBXQGkhrPhGIyJe4oyjWH0kFjUJsgsSC6AeVWRJUyXIEkmmx7eElF+B0e7fJGvUF19LZzrlv8nAAwe5IOcrvC0dSPadws+RMawIuZJD7t9ix3n/4LoQwoDO90b0MavQx6xAeF2GPe9VLLtjsO6/GXv52pMeXxzeg+1DP2fVnakc6HY/gelLueDjHnT77CKCUr4Fu+2ExiPmaF/2vTyAdemTSH/1cowHi2hzw9d0a/82YTPXopXUftlDCzFgejoCrz0dcZvdEsySirF7KUnYRuX/ZSKPOP/c0vQQfUMll/9zhP6/HyHkIjM7X/FgcXwQq8b4kL+5aWU9Cuc4mcvB6ZhH4eBsOJ8n/Q8WQnQ76sdOQogjR/2sAwYCtV/fUjQKo0dPIDc3j8WLPz/puK+++hCDoelekN988yWXC3e10adPDw4e3EVgoPOOEDfeeC2DB1/e8MUVJ3DXG1beGG1g2cd2YrtK3DyhvBgyUwVblmnc/ZYVDydUA/VpNV2tQXZWYmHXHBushN2C1J0ZzRxK9Lsp12eQUPjE6Q6lTnSYiCwbTmTZcMp0+9jnNY99Xu+xJuQ6TNYwWpbcSauSu/CwRTdoHSEEwqM3mseXSPM+bEfewp7/LvaizxAefdEFPojwvrrOhi0VPi3Zc+mrpPd+hvBt82ixYRqdFl1HuW8s+7vdT2aH0diMXifYxGVO7kHmhO4ELkwm4s3VxD7wM9H//YusO7uSdW93zJE+J8bqrmEcE4RhdCC2n4uofDObyqcPUflSFobbAzFNDkGLd875RAgIudBCyIWFFKfq2D3dg/QFbuz9yJ3Q/pUk3ldG+EAzZ68H1NmNcpU4MzkbzmedLhYAQgg71HgH1VZHKgcmSSnnNUFsLnMqF4s2beIaZZ3M4ixu/mYsnw2fR5hXaKPMWRenSpDNZjNGY23F/eblTImjKdm1K/WcdLHIz4I/P9ORulFQXgTu3hDVRjLgdhtBThbureU23vVdRs/n4+j6SCunjin5eD25oz8jctsjGBKCgZO7WLRY9zqt/3yIPycWYDP5OhcYYNk3BKxZGOLWOX2Ms+z1epdNgXcx4OAuvK2JjT5/U2HHSrb7D+z1mkO2+1JAEFo+mNjiCYRUDGw0b2VpK8Je8D62vGlgSQdDDLrAyWh+YxC6ExPXoxF2K0Ep3xK9/nV8M1dhMflxqNN4DnSdSKX3v0/Mo50vALxWHSDyjdUELExGaoK869tx6P4elHYNP+l6tq3lmKdlY/nsCFgk+iG+GO8PRXehl8ubdM35gj1z3Ul524Pygzp82lpJnFxGy5Hl6JunZ805QUFJAbO+ncWEayfU2fTBmTGNPVdjxX6uc6aeg8ZwsQCIAeJwJMc9qn6uvkUCPmdKctycPP/3Kyzfv4rn/3ql2deuljpMnfom0dHtiY5uD5wosfjmm8V06dIXT89wgoJi6NfvKrKzD9c658iRYxkx4lh7FbvdTsuW7XnzzVnHrFtN//5DmDDhQR5++GlCQ+O56KIrAViy5Cfatr0AD48wLr10MJ999jU6nT979zo23xwvsaiWT/z225906tQbb+9IBgwYSnr6vzrJ2iQWS5b8RO/el+HpGU5wcCzDht1ERYVDLPvRR5/Ts2d/fH1bEBbWmhtuGMXBg4dcP9nnAVnp4B0I19xv46EFVp761spDH1i58Qnnk2M4utW0CxILk+OKh/MSi+oKcn026jVNk4dC4wb0dl+8rAlNMn9ToaEnvHwovXO+54qD6SQUPU6BaS0rQwfzS2QcKT5TG8UBQ+h80AXeh6F1CvoWXyEMEdiyHqjSKT+ENGfUeazU9OQkXs/6kStZd/MK8lteRvS6V+j9bgztlt6KV/YGgBPkFyW9okj+fDgbdk4ga0J3AhbvpnPPebS//CP8l6SAvfbngq6jO+7vtsIrpSPGR8OwLS+hbMBuSvvswvL5EaTF+eeQ0V/S7pEyhiTn0uv9QjSjZO09PiyOD2brFE8qDp+brjiNzcJ/FpJyIOWkl92dGdPYczlDY851tnK2n4OTJshSyn1Syr1SSk1Kua7q5+pbppSycbZFn0VkFmcxf/Mn2KWd+Zs/Jqsku9lj+OuvFWzZsp2lS7/kl1++O+HxrKxsRo4cy+2338z27atZtmwJt9xSt374lltuYOnSnyko+Nc26c8/l5OZmc1NNw2v87iPP/4SKSV//rmU+fPfJiNjPyNG3M7gwVewcePfTJw4nscee/aUv09lZSX/939v8O67M1i+/CcKCgq5554H6xz/44+/cu21t3DZZZeydu0f/PbbIi65pC92uyM5M5stPPvsY2zc+DeLFn1GXl4et9xy5ynjOB95vL+RrNSqNtF2x/636psraDqB0Il6uVg4v0nPkVBrdhd1s0IDmsaLq8iwHR9z+0Zt/dzceNha0q7geQYeyOCCnM/xsLZiu/+j/BgVyfrA28k3rmnwGkLo0HyGY4j5B33MajSvwdjzpmFJicW6/0bsZatPenxRRG+2Df2SlWP3cLDLvQTtWUiPj5Lo+vmlBO1ZVNOC/OhEuTLGj72vXs669EnsfXkAbmn5tL32C7p2nE3oO+vRymp/HmnhBtymROKV1gm3GdFQZKP8tnRK2myl8vUsZKHzb3s6I7S6pYKBa47Q75cjBF5gYfvzXiyKC2bNeB8Kt6s+1nXhjAWYszZhjTlXY8V+rnMunIM6E2QhxO3O3poz4NPN83+/UiMst0n7aakiu7mZeO+9GXTo0I6OHduf8PihQ1lYLBaGDx9Gq1bRdOjQjjvvvJ3Q0NobOAwcOAAfH2++/vrfT3mffPIl/ftfQlhY3RKSmJhoXn31edq0SaBt20Rmz55HbGwrXn31eRITWzNixNWMH39qF0Cr1cr06a/Qo0cSnTp14MEHJ7Js2d81Ce/xvPDCKwwfPoz//e8p2rVrQ6dOHXjooUl4eHgAMGbMrQwefAWxsa3o0SOJmTNf4++/V3LggJLLH8+ba8yEt3YktZrm0FNW31xFZxTYXXCxwFilmXeygmzXOSQ8wuaE79wxaDSVWW2pPuWsqx7XhYaRyLIbuDD7D/of2krL4jvJ9PiOP8N7siysB/s852PDNQ/hWtfx6IG+xacYWqehBT6IveQnrOm9sKT1xV74JSeru1T4xpDS702Wjz9AyiWv4l6YTqeFV9Pr/TZEbnobzVLqGHdUVdnm68ahB3uxYdcEkj+8BpuPibiJP5IUO50WzyzDkFW7LZ3w0DCOC8Zza3vcv41DizVR+dhBimO2UPGf/dj3Ot92XggIvcTCxd8VMHhLLjG3l7PvUzd+6BrEn8P8yPrN2Ch7PM4lnLEAc9YmrDHnaqzYz3XOhXNwsgryzONuc4H5wLyq2/yq+5q+bdQZQnX12Fz1Bm22mU9LFblDh7aYTHV3kurcuQMDBlxKp059GTHidt5++z1ycnLrHK/X67nhhmv59NMvAUdF95tvFnHLLdefNI5u3boc8/OuXSl07971GL1ejx6nlPlgMplITGxd83NERDgWi+WYivbRbNy4lf79L6lzvg0bNnPNNSOJiemIr28LevToD0BGxrmnH24ovsGgq6OI5WolWTNq2CpdkFgYHC8/stI5yUS1xEKrT4LcBBVkG5VU6DPxsMY0+tynGx9LBzrnz2DggQN0OjIdmyhhY9BofopqwQ6/JynTncTCzUmEMRp92FSHn3LYNKQ1C+uBG7CkxGPLexNpK6rzWJvJl/3dH2Llnalsu+pTrCY/En+bQN93oon950mMJZk1Y6sTZWnQkXdje7asGM3W32+jqG8Lov5vOUnxM4i/czEeW2uXoAlNYLjKD89fEvFc3RbDMD/Msw5T0mYbZTelYl3tWmdHnzY2LphZzLC0HDo+V8KRDXqWDfLnx6QA0j9ww+Z83n3O4owFmLM2YY05V2PFfq5zrpyDkzUK8a6+ATcBW3BYurnxr73bJmBkM8R5RnB09bia01FFrq6U1oVOp+Onn77hxx+/plOn9rz//kckJiaxefPWOo+55ZYb+PPP5Rw8eIglS37GbLZw7bVDTrqOp+excUgp69VxTq8/1n2jeo66Ksgno7S0lEGDhuPh4c6CBbNZvfo3li51JP5mc8Mtrc41svdCZR0NDg6lCDb8LCh38v1fZxLYXXCxqNEgm51LkGsqyHYXE+QmklhU6B1XJNytLU4x8uzFIH2ILZ5I/8zt9M3+lYDKvuz2eZlfImNYE3Q9uaa/kA3UdwudF7rAyRha70bf4huEIeo4nfLeOo+Vmp7DbW5i3cjVrL/xbwqiLqbl6pfoM7clbX+4A6/Dm2vG1rhfCEHxhdEkf309G7ffQ/adXQn8aiddkubSbvAn+P2UWucnQ11XD9znx+C1uyPGB0Ox/l5M2UXJlF68C8vX+Uir8+fCFCRp/0Qpw/bk0uPdQpCw+k5fFrcOYvuLnlTmnb2ynYbijAWYszZhjTlXY8V+rnOunANntyq/CkyWUi6XUlqrbsuB+4HabSOOQwhhEkK8J4TYJ4QoFkJsFEIMOsn4B4QQWUKIQiHEPCFE3SXTZmLlgbU11eNqzDYzKw40XKPX2Agh6N27B8888yirV/9OREQ4X3zxbZ3je/bsTlxcDJ999jWffPIlV189GC8vL5fWbNs2gXXrNh5z39q16+sV/8no2rUjv//+Z62P7dqVQm5uHi+88AwXX9yXNm0SOHy47ur5+c7jA4xs/bP2l4HiI/Dp//RkpTn3Ru1yBdlYnSA7qUGuSpA1m2sfdAR6pKzPxr6TU6HLAsDNFtboc59pCATBFQPolfMdVxxMI67oQXLcfuOfsEv4I7wre73ewybKG7aG0KH5XIsh5m/0sWuO0inHnVqnLASFURey9epvWTU2hYOdxhOc8jU9PuxCly8vIzBtKUj7CRv6KuIDSH9zIOvTJrHvf5fiviOHdkM/o0uXdwh5fxOiovbnjRZlxO3FKLzTOuL2Rgvshy2U35xGSbttVE7PRha7oFN2g9jbK7hywxEu+T4f/85Wtj7nxaLYYNZN9KZod8N1ygUlBbz44YsnreA155hT4YwFmLM2YY05V2PFfibTXH+/xlyvqXDWOLcVUFrL/WWAs+aZemA/cAmQAQwGvhBCdJRS7j16oBBiIPAY0B84BHwL/LfqvtPGhnF/nc7lnWbVqrX89tufXHFFf0JDg9m4cSv79x+kbduT21CNHHk97733IXv3ZvD11x+6vO748aN5441ZPPzw09x55+1s376Ld96ZD9RP01oXjz/+EFdffTPx8c9z880jkFLyyy9/MG7cKKKjozCZTMycOZcJE+5k585knn32xcZb/BzD3VNycLcgPE5QfATsNrCYwW6FilLB/h2Cknzn5tKZNJdcLKp9kJ1NkI/2QXYJoYcmSJDNWg4ARntwo899JuNha0mHgqm0KXyOA56fkOY9jU2Bd7LD71FalYynVfHdeNgaVlXX3C9Aa/Ep0jIVW9507PlzsBd9gXDvgy7oQYT3NXX6KZf7xZEyYDrpfacQseUdWmx8i87fXkVpQFv2Jz1AVttbsRvcT/BTPvhoXw490IugL3YQPm018eOX0PKpP8i8O4ns8UlYQjxPWEt46TDeG4Lh7mCsiwowv3WYyocOUDklE+PYIIz3hqC1cM7+UggIv8JM+BVmCrbp2D3dk7T57uyZ607EYDOJ95cScrGlXq+lR7sJ3H5l7duGmnPMqZgydkqjjGnsuRprvTOZ5vr7NeZ6TYWzFeTVwFtCiMjqO6q+fwNY5cwEUspSKeVzVa4Ydinl90A6kFTL8DuA96SU26WU+cD/gFFOxnre4+vrw/Llqxg27CYSE7vz8MNP8dRT/+HWW0/eCe+WW24gOTkFX18fLr+8n8vrtmwZzZdfLmDx4h/o2vUipk2bxdNPPwqAm5tzpvvOMHjwFXz99Yf8+OOvJCVdQr9+Q/jjj7/RNI3g4CDef38WCxcuoUOHXvzvf1N59dXnG23tcw3/cJj3iI77LjDw1BUGnhti4MURBqbeYmDOfXo0Hbg5eSFBZ3BRYmF0rVGIrPcmPR3Q+IY7Zs3RN8loD2z0uc8G9NKDViV30i9zCxdmLSOw8uKj5Bc3cMS4suHyC0OL43TKmVj3j8CS0hpb3jSkrbjOY61u/mT0eJQVd6azffBH2PTutPllHH3mRhOz/FkMZf9qjquTZWnUkXNrR7asGcu2n26h+IIIov/3N0lx04m7ewnuO2u/GiV0AsO1/nj+kYjHP23QX+GDeVo2JYlbKbs9Hdv62upLdePXwUaPOUUMS82l/ROl5K0x8MflAfzcK4C9H7vhyr9AYzk4NLcThKL5ae6/35n+fDlpo5CaQULEAd8Bbfi3c14kkAxcI6V0+dqBECIU2Ad0kVLuOu6xzcCLUsrPq34OAnKAICll3nFjxwHjAKKjg5P27Jlb63qN2ShE4TxvvTWbZ599kby8vWja2d1K6lxsFDKpm4EbH7dx4fUN1+h+2X01Xi3cGPRtZ6fGW1JyONh+KkHzbsLrVsfn5JM1CvHbv4xuX/Rjww1/UNDiUqfjsh4ci73kJ4yJjfu32+P9JtsCHmDw/iNnXJvp00Wpbi/p3jPZ6z0Xq1aIX2V34orvI7L0BjQa3khIShuyeCG2vNeRZctB80Hzvwtd4H0Iwymq1lLid+BPote9RlDa99h0JrLb3sr+pAcoDTrWDejo5iPuu3IJf2sNwR9tRVdhJf/KOA7d15PC/q1OemnMvq8S84zDmOflQrEd3UVeGO8LRX+VL0LnWhnYWg57P3Jn91seFCXrcY+ykXBPGXF3lWP0O/l7+IIfF/DX5r+w2WzodDou6XzJCZW65hyjOHNp7r/f6Xq+NFajEACklKlAJ+Aq4HUclePBQMd6JscG4GNgwfHJcRVewNEWBtXfn9D0Vkr5jpSyu5Sye1DQyTszKZqeWbPmsmbNetLT9/Hpp1/x/POvcMcdI8/65PhcJTxO1rTAtdkcXsg2W9XNClYX1Aw6k+aSzVvNJj2ri41CXNQgIwxA40ssrJqjeqm3O9GL+zzB09aKDgWvcOWBA3TOm4VVK2F90G38FNmSXb7/o7JKllJfHDrl647yUx6EPe9NLLtjsO6/GXv52pMdTEGLS9ly7WJWjk4ms8MYQnd9Qs8FHej89ZUE7P25ZnPe0Vrl8jZBpM0azPrUiWQ8czGeG7JoP+gTOnd/l+APtiDquAKitTTh9koLvNM7YZoahT3DTPmIVEo7bsc8+zCy1PmrGnp3iL+rnEGb87h4YT7era1sftKbRTFBbHjQm+LU2uUmjeXg0NxOEIrmp7n/fmfD88XprEU6+FlK+ZaUcpqU8hfpTPn5OIQQGvAhYAYm1jGsBDg6263+vu7raYozgj170hk+/Dbat+/Js8++yPjxo5k69ezWZJ3LPPGllb7DHUmtTufwQtbpqm560Bucn0tncm2THtWNQpy0ebPXbNJz0QdL6EE2voOJTZSiSSOa01s5zh/00ouYknsYcGg7vbN/wNfShV1+z/BTVAs2BI6h0LClwWs4/JQ/w9A6FS3wPuwlS7Gm9cB2+L+nPLY8IIHdl81ixV0ZpPZ9Hq/Dm+jy9UB6fNCZ8G3vI6z/Pseq5RfWYE8OPHUR6/dMZM87VyFsktZ3Liap9QwiX16OPq92Oxjho8N0fyheOzvg/nEM+OuomLyf4titVDx9EPsh5/USQoOIQWb6/1TAwDV5RF1TScpsd5a0C+SfG33JXWk4xoCjsRwcmtsJQtH8NPff72x4vtT5yi6EeBCYJaWsqPq+TqSUrzuzmHD4d70HhAKDpazzXWs70Bn4ournzkD28fIKxZnH66+/yOuvq01xZwslBWAur/JD1jsKaOUlDus3u9Wxac83BIxOSMg1o8Ba7noF+WgN8pgxC+uUWUitKkF21eYNQxMlyOVo0r3R5z2XEGiEVlxJaMWVFOt3kuYznQzPBWR4vU9QeX/iiu8jrHwIwvlazYlrGFuiD3sNGfws9vz3EJ6XOn2sxSOIfb2eJKP7fwjb9Qkt1r9Bwi9jCF33MNntbiK3w3NYPIJO2NB3eFQXDt/RGd9f04l4czUtn1lG1Ev/cPiOzmRO6kFF64AT49QLDNcHoB/hj21VKebXszFPzcL8ejaGG/0x3heKrvPJLTyPxr+LlV7vF9H5hRJ2z/JgzzvuHPjWjYALLLR5oJSoayobzcGhuZ0gFM1Pc//9zobnS50aZCFEOtBdSplX9X1dSCllrFOLCTEb6AJcJqWs011VCHEljkYk/YFM4GtgjZTypC4WSUnxctWq2l3nlAZZ0VDORQ3yu//RISXc/j8bJg8oyoP5j+tJXi0IjIR92wT3zLDSa9ipE98lwzZRcdjM8FU9nFrbXmomw/9J/F8cjO9//t0UWleC7JG3k17z27Htqk853OYm535BwJr1MPYjMzG2q8PwuZ5sChhPpsdCBh3IatR5z3XM2hH2es0l3Xsm5fr9eFriiSu+j+iSUeila9aSjY0070OkjcBYvAezrgDvYo1Qyx0c6voIZYFtasYdrVEG8Nh22KFT/mQbwmIj/6rWHLq/J0UXRZ9cp5xaiXlGNub5eVBqR9ff26FTHuiD0FzTKVtKBHs/dCN5ugcle/R4tLSROLGM2NHlGHxOfbG3oKSAWd/OYsK1E/Dz8qt1zL7sfbz80cs8fuvjRIc6a2BV//UU6jw1BQ3WIEspY6ortlXf13VzNjluCYzHkSBnCSFKqm63CCGiq76PrlrvR2Aq8AeOjXz7gGedWUehUDhPToYgKBJMHmCpBJ9AsJohPklyz3QLvsGSXCebpulc9UE2uSax+NcH2dVGIQaQrladT41dmNFkwzeenW8Y7QEkFD3K5QfTuCDnc4z2ILYETOLHqCi2+f2HMt2+0xKXtBVj3X8NVs84Kjsux6PldiyeUWi5H9Jrfls6fTsE/4zfQcoT/JTLOoSQ+s4Q1qdO5MDjF+K98gAdLvuITr3nEfSpI2muDS3OhNsb0XindcT0QiT25ArKr95DaecdmN/LQbpwRcbgJWl9TzmDt+Zx4VcFeLawsfFhbxbGBLHxES9KM05epT/abqsu5iycQ3llOXMWznE6roasp1Dn6XTi1HUtUZfhpAtIKfdJKYWU0k1K6XXU7WMpZUbV9xlHjX9dShkqpfSRUo6WUqoGnApFI2N0+3cjnq5Kb2yzQKuOkvA4iEqUVJY5V8nSmQQ2F2ze0GkghAs+yPW0eRNGwIaUDXfqOCYeLAjpgkhbcQwaeiLLbuCSrJVcnLmS0PIrSfV5k58jY1kTdAN5puUNtolzFint2I/MQNoK0bf4DOHWjrLAdhSH9mBXn5Gk934Wn8zVdP1yABd8lETojo9qnodHyy8soV7sf+4S1qdOInXmILQSCwl3LKRb4kwiXl2JrqCi1vWFvx7Tw2F4JXfAfX4rcBdU3JNBSdxWKv57CHu28xIhTQdRwyoZ8Hs+l6/II2JwJbune/B9YhArbvElb+2Jykpn7Lb2Ze/jUO4hAA7mHiQjO+OEMc5yptt7nSmo83R6cVb4VSiE+EkI8bgQondjJMwKheL006qjZO9WwYFkgabBtr8FpUWC4Kh/E5NKJxuk6YwuulgIAUad8wmyrn4aZIdpDo3eLEQKq9qg10gEmHtxQe5nXH4wjfiihzjs/jN/h13IX2G9OOjxBXaauE28LQfbkZnoQv/dPyGtRxCaL9KjM+l9nmPFuP3svHwOmrWCtj/eRp93Y2i5+mX0FfknVJTtHgay7+rGpi3j2fndDVTEB9Dqid/pHvMWrR78GVN6Qa1hCKOGYWQgnqvb4vFzAroenphfyKQkfivl4/di2+5at8LA7lb6fFjEkORcEu8rI/NnI7/0DeTXfv4c+M6Evepf7+gNU3VtlDq+atyQKrIz6ynUeTrdOJsgXwusxWHztgwoODphbqrgFApF03LlOBs2KzwzyMDLN+mZOtJAi7Z2elZpjuO6SUJbOVfF01x1scDRLESaXZVYuOpiUZ0gN67MQmLHBSMghRN42KLpUDCVKw8coFPeTMzaEdYG38gvkbGk+LyCWRQ0ybr2/PdB80bn+6+2XVZsRFoPgiHcMUbvRmancawetY2VQ8ayrT1Er3qcvnOiaP3bJNwLUoFjLeLQBPmDW7P951vZvHosede0IWz2erq1nUXijV/jvbL2PQ1CCPSXeuPxXTyeW9tjuCMQy2dHKO26g9IhKVh/LcIVEynPaDtdXi5hWFouXV8tpvygjn9u8GNph0A2TK/gn80nt9s6unpcTX2ryGeDvdeZgDpPpx9nfZB/kVI+JaW8EPDDkTAfAqYA/zRdeAqFoinx9IWHFli57z0LHS6288xCC2On2jCYHI8P/4+NAbc7l/S6bPNGlZOF0xVkR1D1k1gAjV6FtCOkSpCbAr30IrZkApcd2kXPw4vwtLZmu/8j/BQVxWb/SZToG3enu6zcieY99N+fzfuwl/wI6NF8HB1IaxJSoVERP4O8Vpfw++VebL0ggcgtc+j1Xms6LLwO3wP/HOOnXE1p1zD2vD+MDSn3cvCh3vj+sZeOlyyg40XzCfxqJ1hr/9/RJbrhPqMlXqmdMD0XgX1LGWWDUyhN2ol5QS7Shf85g7ckcXIZV+3Ipc8nBZiC7Xz7+2Kslccm28dXK+uqFteninw22HudCajzdPpx+tVdCBEqhLgRR6OQmcBNwHIcSbLiNNO//xAmTXr4dIfhMrGxnXjttemNNt/Zeh5OJwYTdO4nGTLBTnQ7SVkRVBzVGdfZQpXO6FqraXAkyM5KLGoqyHZXE93qCnJTXKZ3zWlA4RoCHeHlQ7kw+3cuPbSRiLLh7PWew68RCawKvppc05+NolMWnhchzY4KsJQ2bAXvISu3owuciBAaUtockiAcibLQ3NBHfYI+fhPZIRZ+GRTCzr634n/gT5I+v4jun/QkZNfnCLv1BPmFOdKHjBf6sS5tEmlvXoE+t4zEkd/Qrd0swt9ag66o9iskWpAe0xPheKV05Cmfl5i47f8Yd9dDjPYezSjjHYwy3sHkFjfUeuy+7H3c89o9NRVfTQ/RIyq5/K98bP22IfXHXsU53m4rp6D2Bi+HCw7Xev/JaGx7r+N/t7ooKCngxQ9fbHAFtrHmOdVcTWGD1pixnw84JaATQmwHWgFrcEgsxgMr1ca5pmf06Ank5uaxePHnJx331VcfYjCcfXrI1at/x9PTee9PReNjqYRtfwk2/qpRkC2QErz8oXWSnc4D7ARGODePZtCwmeshsXDWxULokAiEyxKLqgpyEzhZKJoPP0sXkvIW0L7gZdK8ZrHXezb/hC3Ct7IrccUPEFV6Y73bWQv33sjcV7CkJoHOD+zF6AIfRvMa6Hj8uG03UkqEEAhjHMJzAPaiLznYZiCHk2YTtv1dojfMoMOSm6j4K5r9XSdxqNNd2Ey+J/gpZ024gKzxSQR8n0LEm6uJ+c8vtJjyF9lju5B57wWYo31PjNWkUVTkWevvUZTtji25Al3iscblR7tPvDDuhWMee3Gyo7FKSbrG7umepM13w1qiEXKJmYNhpUQMMjP3kbmAozXwso3L6Ne1X71bAk8Z27g1tZP9bkdztBtEQ9oZN9Y8p5qrsc/TqdZTnIizFWRfwAaUAaU4Otqdd+82ERE+6HR+J9wiIk5fi2uz2fFnCAjwx9v7zGp5a7GcumIXHByEh8eZkyDb7fYTPrWfy5QVwcwJel69zUBJviCitSS6nUQIyafP65l2p4HMVOfm0pk07GbpkjYSg/MJMkJg15vQrC4myJpKkM8l3GzhtCv8HwMPZtA5bzZ2UcGGoNv5OTKG3T4vYdaOuDyn5tYeY+tkNP/x6AImo2/xHZrv9bWOFUIghMBevhHL3oHI8lXooz5B53cLdoMH+wL/5p9BQ9k87BvKfWNo/dfD9H2nBfHLHsStcG/NPDWV5QWjOXJ1Itv+uJ0tK0aTf2UcEW+tISlxJq1v/RavdYdqjaMuSjtup+yaPVj/LEZK6bT7hFeMnW6vFzMsLZcuLxdTnKrj72v9WdopkD1z3cnNOfMcFZz93RrLDaIxXSWa26FCOWK4jrMa5CigG/AtDh/j74AjQohFQogHmiy6M4zs7NpPV133NwWjR09g6NAbmTr1TaKj2xMd3R44UVrwzTeL6dKlL56e4QQFxdCv31VkZ9d+OWzkyLGMGHHsp0m73U7Llu15881ZgKNi8sor02jduiuenuF07tyHjz76t6q9d28GOp0/n376FZddNgxPz3Deeed9CgsLuf328YSFtcbDI4z4+C5Mm/Z2zXHHSyyKioqYMOFBIiPb4OERRvv2Pfn882+O+b06d+6Du3soLVu258UXXz1pQpafX8CoUfcQGNgKT89wrrjiGrZv31nz+Pz5n+DjE8XSpT/TqVNv3NxC2Lkz+aR/g3OJPz/TOJIpeCfZzOR3rNz0pI3rH7Ux7g0bc5PNBEVJFk5z7sqEzuT4P3BFZuGKxAIcOmTXN+k1VYIsgMa1jlM4j066E1Mynv6Z2+id/QPelvbs8H+CnyJbsDlgAiX63a7PGTAOzedqhCECW+Gn2HLfqHns6NcZe/GP2LIeACHQR3+PVtW9z3bkHbBmIkt/JdN2F+suG87aW9eRGzuUqI3T6f1eHO0X34DPoVXHrFtdWS7pHkHKR9eyPvleDk3ugf+PqXTq8z4d+n1AwMJksJ36+WZ8KhzbmlLKLt9Nac+dzF4w65jHT6UbNvpJ2jxYxtDkXHp/UIjeS7LuXh9mTPoZu8VxDs4ULayzzhqN5QbRmK4Sze1QoRwxXMfpzE5KuUdK+S5wB3ADjiR5EPBq04SmqIu//lrBli3bWbr0S3755bsTHs/KymbkyLHcfvvNbN++mmXLlnDLLTfWOd8tt9zA0qU/U1BQWHPfn38uJzMzm5tuGg7A008/z7x5HzF9+its27aKRx99gHvueZAlS346Zq4nn5zC3XePZdu2VVx99VU8/fQLbNu2g0WLPmPHjjW8++4MIiLCa41DSslVV13PX3+t4L33ZrBt2ypeffV5jEZHgrN+/SZuvHEU1147lM2bl/Pii8/y8stvMnPm3Dp/t9GjJ7BmzXq+/fZjVq36FXd3dwYPHkF5+b92SRUVFbz44qu8/fYbbNu2ipYtW9Q537lGaYHAzUPieeKVXAD8QiSlBc7NpRkdGk1XZBbCqIM6mijUhtSMCJdt3hzPH9nICbJAQwqVIJ9uqttZ9z38M/0ObSGy7Eb2eb3HrxFtWBV8NTluv9dLpyyMCTUOKNWSCint2Ao/x3rwNoTnxejD30Hogx1jrHnYCxag+d2JIX4z+hbfYTsyjXyxkB1XfczKO9PJ6P4fAvb9TPdPe9Pt074E7/6aaq+1o+UX5mhf9v3fZaxPm0T6q5djPFBEm+u/omuH2YTNWnvSuN2eicArtSNub0ez35RFpiX7mMeddZ/QDNDypgquWHmE7j+ksr/Dr9iE42qPzWbj702ntwrprLNGY7lBNKarRHM7VChHjPrhrAb5AqBf1a0vYAI2Aq/h6HanaEbc3Ey8994MTCZTrY8fOpSFxWJh+PBhtGzpaAfaoUO7OucbOHAAPj7efP31IsaOvQ2ATz75kv79LyEsLJTS0lLeeGMWP/74NRdd1AeAmJiWrF27gVmz3uWqqwbWzDVx4jhGjPi3VfC+ffvp0qUTPXokAdCqVd3tSX/9dRkrV65l69aVtG2bCEBsbKuax994YyaXXNKX5557HICEhHj27Elj6tRpTJw47oT5UlJSWbz4B/7443suvrgvAB98MJtWrTry8cdfcuedjqq5zWZj2rSpJCV1qTO2c5WYTpI132v88bFGn2vtmCsc79d2O2z+TSN5jcaA25xLYHXGelaQnZVY4PBCdr2TXlNVkDVopkYWCufwtXSkW9482uW/RLr3TNK93ybLYxG+5i7EFT3okk5Zc08Cd8frliM5tmLLvBdZuQvN/270IcdqRGXFeqQtD3v+HDTvQWieF2JsvQdpKwGgwiuS1Iv/j729niZ82zxabJhGx8UjKPeNYX+3+8nsMPoEjbLNx0Tm5B5kTuhO4HfJRLy5itj7fz5l7MJdwzg2mA+tv0LecQ9KmP3lbF6c+GKtx54wl4Dllq/BYHMILauwmiVvP/Yjo4bdTtjl5pN11G4STuascbQW+WRuEK7ocBtrnsae60xc71zB2V1dy4H1wJ/ANOBvKWXpyQ9RNBUdOrStMzkG6Ny5AwMGXEqnTn25/PJ+DBhwCSNGXE1wcFCt4/V6PTfccC2ffvolY8feRmVlJd98s4g333wZgB07kqmoqGDw4OtrdnKDQ2N8fMKblNT1mJ/vvnsMN9wwio0bN3PZZf0YMuRKLrmkb61xbNq0hfDwsJrk+Hh27drN4MFXHHNf3769mDLl/ygqKsLH51gt+M6dyWiaRu/ePWru8/X1pWPHdsfIKPR6PV26dKx1zXOdpCvtVJTC3If0vPsfCG0l0TQ4kiWwW2HEo1b632ZHSk75BlhTQXal3bQLm/TA4WThcoJM0/ggC6lDcv7o1c8m3OyhtC2cQkLhE+z3+phU79fZEHQ7O/weI7Z4Iq1KxmG0B7o0pyxfh73oS/TRixFu3R33STtCOD4YCvc+lLf6nl0HLqVzel+MUZ+juSchdF5VE5ixl2/GZk7mQLfJHOhyL8GpC2mx7jUS/riPmBXPcKjjOA50m0yld9QJyXLeiLbkjWjr8E4enAWlYScG6ZV1zI85hbW4Twg4nJdN2fWpGO8P5cGbxlCU7X7CMJ/Qct7a/wVQu6OC1FvJNO7mzyH++LazknBfKa1urkDndsJUTYKzzhqN5QbRmK4STeFQcSatd67gbILsrxLiM4dTbWrT6XT89NM3rFq1ll9++YP33/+IJ5+cwh9/fE/nzrUngrfccgMXXjiQgwcPsXr1esxmC9deOwRw6JEBFi78lOjoqGOOO94543hHikGDLic9fQs//PALv//+F0OH3siIEVczb97ME2I41eau6suctVHb/Seb7ujxJpMJne78bQ7Zd7idvsPNZOwQZO91nJegKElMJ8cJdCY5hn81yC45WRh1yBLnE1e7zuS6i4VW9WGySSQWKkE+k9HhRquSsbQsGc1ht5/Z4/M6O/yfINn3f0SXjiau6H68rK2dmkvz6IUh4QBC86hpW+6wgHMkyULnxZKS1/nbPZP7yxOJL/mppgJtL9+E7fBjYM0GYcSW/Sj6qM/JaX0dOa2vw+fQKlqsf4Po9a/RYsMbHE64gYzuD1ES2g1wyC/cxiwAoLh3FPPzf8KUlk/4jLWEvr8JXamFwktbcuj+nuTb40Fz/MNWu08cjf2QGfOsHCx/51C2sIAiTkyOgWOS5rocFWyVkNGlkOTpHqwd78vWZ7yIH19O/Pgy3IKb9upKbb9bbTSWG0Rjuko0hUPFmbTeuYKzm/RUcgyEhtb+xl/X/acTIQS9e/fgmWceZfXq34mICOeLL76tc3zPnt2Ji4vhs8++5pNPvuTqqwfj5eWofLRrl4jJZGLfvv3Ex8cec6uWcJyMoKBAbrvtJt5/fxZz577FBx98SmXliUlO166dyczMqnOTXNu2iSxffuzmluXLVxEVFVGrg0e7donY7XZWrlxTc19RURFbt+6os0p9PhPdTnLBYDsXDLa7nBxDPSUWRr3TnfTgzJJYCPRIGrd9taJpOFGnfDP7vN7l18gEVgYPJce0zCmdstAcBYDqqjGALFuBtGRSaMtkddk8JHaKrclUmh3VOXvFNuxH3gLhjj76Bwyxq9F8b8Ze8u/+jaKIXmwf+jkrx6ZyoMtEgtIW0+OjJLp+filBexaBtJ/gp1wZ68/e169gXfpk9r7UH7c9R2h7zRd06TSH0Lkb0MpqdxHSIoy4PR/p0ClPa9h+C50JYm6vYOCaI1z6Yz7+3axsm+LF4rhg1k7wpmjX+Vt4UJz9nH3GuaeRQ4eKTncITrFq1Vp+++1PrriiP6GhwWzcuJX9+w+eMikcOfJ63nvvQ/buzeDrrz+sud/b25uHHprII488jZSSiy/uQ0lJKatWrUXTNMaNG1XnnM8++yJdu3amffs2WK1Wvv32e2JjW9UqERkw4BJ69uzO9dffwWuvvVCjMS4tLeOaa67iwQcn0rNnf/7735e5+eYRrF27gddfn8kLLzxd69qtW8cxbNhg7rnnQWbPfgM/P1+eeup5fHy8GTlyhHMn8zzHFV1htcTC7tImPec76UH1Jj0XG37UJMiN2yhESSzOThw65fdol/8i6d5vk+49i+Vh/fCt7Ep88YNElt7gtE5Z2sux5b4MWPnRpwVWIWlnBp2UbBT76AvYCz8BWYku8CGEwSGLEG5dsOe9gQx5DiH+fRuu8G3Fnn5vkN7nOSK2vkuLDW/RaeHVlPm3Zn+3B8hsfzt2g+cJ8otDD/Umc3IPAr/aScS01cTd+wPRzywja3wSWXcnYQnzOiF24anDeE8I3Neg0+mYS0BYfzNh/c0U7dKxa5oHez9yJ/VdDyIGV5IwuYzQfs2vU1YoGoLqk3oO4uvrw/Llqxg27CYSE7vz8MNP8dRT/+HWW+t2sgCHzCI5OQVfXx8uv7zfMY9NmfIkzz77GK+/PoOOHXszcOC1fPPNYmJiWp50TpPJyNNPP0/Xrhdx0UVXUlxczMKFn9Y6VtM0liz5kj59enL77eNp374nDzzweI3Xc7dunfn88/l8880iOnXqwxNP/JdHH72Pe++9q871582byQUXdOOaa0bSq9dllJeXs3TpV7i7135ZUVF/qivILrlYmHT1qCBXuBZYTYLcuH2NBHrsQlWQz1YcOuXnGHhwH13y5mAXFawPuo2fI2PZ7fMyZi3/lHMIzR19i6+x6Py4IvNdbi02M7oYDugl37OCorK/kJXJCPceaJ4X1hxnL/oOYeqIEPoaucbR2Ey+7O/+ECvvTGXbVZ9hNfmR+NsE+r4TTew/T2IsyawZW50sS4OO3Js7sGXlGLb9eivFvaOIeukfkuJnEHfXYjy2ud71ruyWNGxrXbuA7NPGRo+3ixmamkOHp0vIW2tg2ZX+/NQjgPSP3HB5C4FCcZoQLpn6n+EkJcXLVateq/WxlJQo2rSJa+aIFOcSu3al0rr1gdMdxhlLxk95LB26iWv+TCKst59Tx+Te9QXlv+6mRfpTNffNm3d1neO7ftEfYTOz4eZ/nI5LVu7EsqcduqhP0fne5PRxp2KL/2T2e37IVQdOnUgpznwkdg67/cQen9fJcf8Vnd2D6NJRTumUPymcQHLJu0RYLeRrsNcAOoxcJwZycVkh+oi5CFMCAPayVdgy70UX+mJNp75TByfxPbicFutfJ3jPd0idgew2N7O/2wOUhHQ+Zmi1VhnAbXceEdPXEPzBFnTlVvIvjyXzvh4UXB5bc3lolPEO6uItn/uhyI6ujyfG+0LRD/ND6FwrA9sqYO+nbiS/6UnRTj1u4TYSJpQRd1c5poBzJ/9QnD2MMo5aL6XsfqpxqoKsUCgaBZ2p2gfZFZs3VyvIJjQXfZARTbVJT49UFeRzBodOeRB9D/9Cv0Obq/yU3+XXiERWB19LrunPOnXKaZaVZOssbDQ5kmMAG2ZsFevAlo8wJdRsQrblTkW490QY27oQnKAw6kK2Xf0Nq8bs5mDHcYQkf0mPD7vQ5cvLCExbClWV6KO1yhUJgaRNH8T6tEnsm3IpnluzaTfkM7p0nUvI/E2ISis+oeW1LukTWo53eidMr7fAfshC+Y1plLTfhnnmYWSJ89IinRvEja5g0KY8Lvk+H9/2VrY87c2i2GDWTfameI/SKSvOTOrUIAshHnR2Einl640TjkKhOB0s/1pj71bBLc/VX1P7byc9FzatutxJz4g4QzbpadKAXTSurllxZuBr6VTlp/wiaT4z2Os1m8yw7/Cr7E580YNElI1Aq7YPBIqmboRatqjsil1NvxueRNpLAQPWnBeQlTvRBT2MMNa+wfmRR6Colrl8fGDqVCj3jydlwHTS+04hcvMcojZNp/O3V1Ea0JaMpAfJbncrdr3Da63a/cIa6MHBx/py6IGeBH2+nYhpa4gft4Top5fxzd0ryRqfhDWoNnckHaaJITz88kSH20Ua8EDVDfAJKuOtQ186dU6FgPArzIRfYaZgq57ktzxIm+fOnjnuRF5VSZuHygjqYznjdcoFJQXM+nYWE66dgJ+X3+kOR9GEnKyCPMnJ28QmjlGhUDQxW//UWDqnYZUcrVqD7IoPskEHTe2DrFwsFPXEzR5Gu4LnGXhwP53zZmPVilgXPJJfImNJ8Zlao1OuLaEFSN7bFaEPwZIciTVjMPbCL9BHzELz6F3nmnXNdfz9Vjd/9vV8jBV3prN90IfYdSba/nIXfd6JJmbFcxjKHJrjozf0SZOenNs7s3ndnWz/YSSlXcOI/u9fJMVOJ3bCUtx35da+9uE6rOByPSi7PR3bxrI6f5/a8OtopefcIoam5NLusVJyVhj5rV8Av/QJYN9nbri6D7c5WfjPQlIOpKhWzecBdVaQpZQxzRmIQqE4feiNEmsD97DpDPVpFKJHVrpQQdaMaK76IFcnyPZG3qQnDUhhQ2JHKLXaOY1OuhNTMp5WJXeR7f4De3xeY7v/o+zynULLkjuBN2s9zmY3oo/6BHvFVrAVIkxtEPqgk3q6u4rUGcludyvZbW/Bb/8yote/TszK/xK95mWy291GRtIDlB3neoEQFA6IoXBADO47coh4aw0hH24h7N2NHBkcz6H7elJ0aUunbGys3xdg/ewIuku8HDrlwb4IzbnfzT3cTqf/ltLu0VL2fuRO8lserLzdl81PepFwbxmxY8sx+p45OuXqls1SSv7e8jfDLhymqsjnMOpVXaFQYDCCpYEF1n8lFq5pkJESaXUuSXY0CjkzNMiadCTeds7gcpeiURFohJVfxYXZv3PpoY1ElF1HuveJTY+OR3PriOZ5IULv6GZa3+TYXrb6JMEJCqL7seXaxawatZOs9qMI3fkRvea3p/PXg/Df9ytIeYKfcnm7YFJnX8X61ElkPH0RXusy6TDwYzr1eI/gj7YiTiGB8k7riOnlSOxplZRfl0ppx+2Y5+Qgy5z/oKz3gPhx5QzeksdF3+TjFWtj02PeLIoJYsNDXpSknxmpytEtm6tbNSvOXZx+1gkhAoQQI4UQjwkhnjn61pQBKhSKpsdgAqtZnLT74KmokVhYXPRBBqd1yHa9qf4V5MZOkKs0qFLpkM9L/CxdSMr7gCsO7m22Na3pvbCk9cVe9A1S1v0/UxbYhuTLZ7Pirv2k9f0fXoc30vWry7ngwy6EbZuPqLpcdLT8whLiyYGnL2b9nonsmT0YzWyj9ZhFdEuYcdKYhJ8e04NheO3qiPsHMeCro2JSBiVxW6h45iD2TOf/P4QGkUPM9P8lnytW5xE5tJKUtz1Y0jaI5Tf7krvKcOpJmojq6nF1y2abzcbfW/6moKTgtMWkaFqcSpCFEL2AFOBV4H/AGOBJ4D+A6rigUJzl6KtySGsDcr2aCrILEgtMVQmykzpkR6MQ1xJdIXSAhmxsDbJ0vFnbhTJ2PZ9xt0We9HGLaLwGU7qwaUhrJtb9w7GktMaW9xbSVlL32h5B7O31FCvu2sfOgfMQ0k67n0bT591WtFz1AvryvBMqytJNz+ExXdm0aRw7Ft1Iedtgp2ITBoHhpgA8l7fB4/cEdH28MP9fFiWtt1J+515sW1zTKQd0tdJ7QRFDd+eS+EAZWb8Z+fXiAH652J/9X5uwN7P8/+jqcTWqinxu42wnvVeAj3H03CkC+gOlwKfAe84uJoSYCIwCOgKfSilH1TFuVNW8R/vPDJFSLnN2LYVC4Tw1CbLZIbeoD9Wd9FyyeTNWbQx0toJcn016joUavVGIklic2ZzKDaJ5kPwU1YKWJWOJK7qP5x5qecqYhKDWKzlCgC5wMlrAvcji77Dlvo4t6z5sh59F878LXeAkhOHY1tH33FM9lwkYXXUDgZ3kUh2tVr9AZvs72N/tAbJ8vXntlXnc6fc5vrow3MYsoODKeAqujMc3rITCIyd246vNIk4Igf5Cb/QXemPfU0Hl9MNYFuRh+SAP3WXemO4LRXeFj9MyE48oO11eKqH9k6WkL3AjeboHy2/2w7OVjYRJpcSOqsDg3fQ65dSDqTXV42psNht7Du5p8rUVpwdnE+ROwFgppRRC2ACTlDJNCPEo8AmO5NkZDgHPAwOBU7UyWymlvPAUYxQKRSNgqJLpWirB/cT3QaeoriC7tEnP1Qqyrh4SC8dCjZ8gV7UjVhXkMxNn3SCaFkFY+RDSvKeT5v0WRUW1P8+PjqkumVP1/ULoED7D0XyGYy9bhT3vDex5r2PPewPN9wa0wAfR3JNOPhcaq+/YRov1bxCxbR6Rm+fw2IBo9oRmsLRkCjf7zjpGfjEty9F85MOv3+X3Xf9w45ZApnwbQElUOAc/78mR69ogDSe64GjxbrhPi8bt2QjMc3Mwz8qhbOgetLZuGO8PxXBzAMLNOaWnwUuScG858XeXc3CRieRpHmx8yIdtU7yIG1tO63vL8GzhwtUrF5kydkqTza04M3FWg3z0O0A2UN1fuASIcHYxKeU3UsrvgDxnj1E4R//+Q5g06eHTHYbiLMVgcryTWhqQQ1a3mnZpk15VBdlpDbLOhJB2sLvo1yyMTeKDDCBVgqw4Cd1zP+byg2nEFT3Q6HNrHr3Qt/gcQ+s9aAETsRcvxprWHUv6pdiLTn7pvzSoPbsGvsvyuzJY3/c+lgbvQwrJqpLZGHfNRNj+vTJSMe8OCkoK+Ct1NVLA10lFrJ12EbrCShJv+45ubWcR8foqdIW1t4EXAXpMj4bjldIBt3mtwCCoGL+PkritVP7vEPYc56/CaDpocW0lly3L5/LleYRdZib5TQ++Twhixa2+HNngbN1PoTg5zibIG4ALqr5fBjwvhLgDeAvY0gRxAXQVQuQKIXYLIZ4WQtT6rBdCjBNCrBNCrMvNbdbSQLMwevQEhg698ZTjvvrqQ1588fTtl9Tp/Pnqq4WnbX1FwzhaYlFf/pVY1GOTnpMVZLvOEWi9NuopFwvFacLD1oIOBa802fzC2Ap9+BsYEvajC30NaUnHur/ulu1HY/EMZXbbSqy66uez5NfsifR+N5boNVPRVxQA8M3cZOxWx/+4Xdp5L2YvG7fdzc5vrqeilR+tHvuN7jHTafWfXzDtLagjTg3jrYF4rm2Lx0+t0V3gSeX/MimJ20r5Pfuw7ay9q19dBF5gpe+nhQxJziVhUhmHfjDyc69Afhvgz8HFJmTTFZQV5wHOJshP4pBHADwF5ADTAX9gfBPE9RfQAQgBhgM3A7WWR6WU70gpu0spuwcF+TRBKMeSnf0lq1d35K+/Ali9uiPZ2c51EWoqzGbHm35AgD/e3t6nNRbF2Uu17thSWX9vViEEmkG4tkmvpoLsrMSiIQlyI/sgK4mF4jRjE+UU63dSaNgKgND5ogt6EEPrVHRRnzo1R6Etk5Xl72OrulBs0cFXCUb2h7Yi/u9H6fNOFAF/jWVl+byaMTUODmWF5A9JYPuvt7F59RiODE0gbNY6urWZRcLN3+C1+mCtawoh0PfzweO7eDw3t8NwWyCWj/Mo7byDsmEpWH8vqmnN7QyeLe10nVrCsLRcur5STGmGjr+H+7GkQyAps92xurY/UKEAnEyQpZTrpJR/VH2fI6UcJKX0qUpMG72CLKVMk1KmSyntUsqtwBTOALeM7OwvSUm5j8rKA4CksvIAKSn3NWuSXF1Rnjr1TaKj2xMd3R44UWLxzTeL6dKlL56e4QQFxdCv31VkZx+uc945c96nTZvueHiEERoaz5VXDsdq/Tdpef/9j+nQoRceHmG0adOdN9+chd3uSIRiYzsBcOONo9Dp/Gt+rp43IaEbbm4hJCR0Y+7cBU6vu3btBgYOvI6QkDj8/KK5+OIrWblyTQPPoKI2jtYgNwSdSXOtgmxy0eZN5wi0Xl7ITVVBVgmy4jRQpstgTfBwNgbexYrQy1gZMhiLKAZACD0635ucmmdJyf+wc+z/rE3A1H6dWHPbRnJaX8c34n047kOp3Sr4du7uGq1yaddwUhZczYbd93LogV74/ZpGp4vm0+Hi+QR8swtstb8u6Nq64z6zJV6pHTE9E45tQxllV6ZQ2n0n5g/zkC68nhh9JYn3lTFkZy59PirA6C9ZP9mHRTHBbH7Ki/LMM8NPWXF24JRYRwjxO3CdlLLguPt9gO+klP2bILajkcBp79C+d+8U7PZjLwHZ7eXs3TuF0NDrmy2Ov/5aga+vD0uXflnrp+ysrGxGjhzLiy8+w3XXDaOkpIRVq9bVOd+6dRuZNOlh3n9/Fhde2IuCgkL++OPvmsfnzl3Ac8+9xLRp/0dSUhe2bdvB+PH3YzDouffecaxe/TthYa2ZM2caQ4YMRKdzVAW//fZ7Jk9+hNdff4HLL+/Pzz//zsSJ/yEsLIShQwedct3i4hJuvfUG3nzzJYQQzJw5lyFDbiA5eT1BQYGNeEYVjWHzBg6ZhUsuFlUJstMuFlp1BdlVqzdjo9u8qQTZNZrbVcLHp+71XOFfJ4hjEQLeftu1uU7mUOEKjz1dQttnrqFsTQKpn7xCSUZ7uj5zNX+vXcwjV4889XrYsOy9El3gg6RZVtRUhquxYSbVsoKSkJnsHPQByw9vwGLffuIY83LAoVF2G+MofpijfNj3Un/2P3khIfM3EzFjDW1u+pqKGD8yJ15A9qjO2L1NJ8SkBRswPRWB8T9hWD49gnlaNhVj91L59EGMdwdjuCsYLdA5fbGmh+gbKmlxfSW5KwwkT/Ng0+wK5udMZaj9Abrea8K/i2oTrzg5zqrZLwVqM39yAy5ydrEqHbEe0AE6IYQbYJVSWo8bNwjYIKXMFkK0AZ4GTq+WAaisrP1yUV33NxVubibee28GJtOJLzIAhw5lYbFYGD58GC1bRgPQoUO7OufLyDiAp6cHw4YNwtvbm5YtoXPnjjWPv/DCK7z88nOMGOHQtMXEtCQtbS9vvz2Pe+8dR3CwozuUn58vYWGhNce9/vp0br31Ru69dxwACQnxrF+/iVdemcbQoYNOuW7//hcfE+dbb03lm28W8+OPv3LrrafWZSucR29s+CY9cGzUs7ukQa6SWDjtYnEmapBVguwMze0q0VhJ96lcJQBmz268uU45B5KAftMxeOWz+eXP/r3fasQ9/k/g3wS5tgReWo9gz38H2/+3d57hUVVrG77XnpbeCyEFSKP33gRBwIrYG2IDjwVF9OjRz67HflQUKxbsvWIFVATpvZdUSCW9l8mU9f2YJASSwEwabd3XNVcye1abTdjzzruf9byFu7Cmnct9pp7oAt9B852O0NyanPPBkJ0AaJYKwnZ+QOTml/EoTqbKp5iMQS+T1eemw1wv3G78ELuXkYOzh3Lw1sEELEqg87x1dLtnKZFPrCDnpoFkzx5KTUTjbyvCTcN4QxCG6wOxLS3FPC8H8yNZmJ89iGFGIMY7QtDFNb3ORmMJCB5tIXh0CXu//IiipF0s3/oducNmEzrBTPc5lYRNqUGoxLKiCY76ZyGEGCSEGFT7tF/d89rHUOBmwJXo8CEc3sb3A9Nrf39ICBElhCgXQkTVtpsIbBdCVAC/At8BT7swT7tgMjVtCN/c8faiT5+ezQbHAP3792HixPH06zeaSy+dwZtvvkdeXn6z7SdNGk+XLpHExAxg+vRZfPjh55SVOW7V5eXlk56eya233o2PT0T944EHHic5OfWo69yzJ4FRo4Yfdmz06BHs3r3vmPMC5Obmccstd9GjxxD8/aPw9Y0kNzeP9PSMY54jhWvUSSxas0kPwBRgqK+o5wwtcbEAXC4W0i4+yLU5A+VioehIzFouURe8TsIHz9QfM3gVYqnwpSKj+2FtJY0jb6EPQBd8P4a4/ejCP0YIN2xZs7AkRGHNfQxpbV6KZzd4kjnwdtbesI/tU7/H7B1F3N93M3pBBLF/34OpNA3g8OIjOo3Ci3qwc/l1bF95PcVnRdN53joGxb9O3Iwf8Nyc3eRcQgj0k33x/DUez829MFzmj+X9fCr67KLy4iSsK8qc1ikXlxez7sA/ICRZQ5YQ/WQ6pfv0rLjQn98GBJL0rjtW1/YHKk4DjvVJthHYgEPisKT2ed1jHfAADn2wU0gpH5NSiiMej0kp06SUXlLKtNp2/5ZShkopPaWU0VLKR6SUx32reNeuj6Bph9s3a5o7Xbt2rHuEh4fHUV/X6XQsXvwdv//+Lf369Wbhwk/o3n0w27btaLK9t7c3Gzcu54svFhIVFcFzz71Mr17DycrKrtcZv/HGS2zevKL+sX37anbsWHPMtTZlBl937GjzAlx//a1s3LiFF198ipUrF7N58woiIjpTU3Pc/xROOdpKg3zF1hGMfaX7sRvW0nIXCxeDUq09Ncjq71HRcaR5LcRa5cXB5Yc0xt6xW3ALzMRc1AkAWaspFrXKxDL9Pmzi8AhQaEZ0ftPRR29C3/UvhPtw7HmPOwLlzFlI857mF6HpyI+bxuYrV7DhmvXkR59PxOZXGPluNL1/vhLvgxvqmzbMLJcPCyfh84vZvO92Dt4+BP9fEuk/4n16T/wY/58SwN50wKvr4477O13xSuqL8f5O2NaUU3lWAhWj9mL5ohBpOXqg3LAKnh07e/t/wfn78hmxsASdm2TjbT78FBPMjic8qc5R6WSFg2P9JXQDYnDof4fVPq97hAM+Usr323WFJxChoZcRF/cKJlMEIDCZIoiLe6VD9cfOIoRg5MhhPPLIf1i37i86dw7jq6++b7a9Xq9nwoQzePrpR9m6dSUVFRX8/PNiQkNDCA/vTEpKKrGx0Y0edRgMhkZVhnr2jGfVqrWHHVu1ai29eh0KoJqb19F2HbfffjPnnTeF3r174u3tRXZ2TlucHsURHAqQO1jq34JCIdASiUU7FAqpl1i07bgKxdEoM+whd+3U+uduIQcIHvw70q4nuzZoljiuxbluS9kUOIOtgTP5o3M8+3wa34gVQqB5nomhy08YYveg+V2PveQTLEm9sBw4B3v50qNmass6DWX3eZ+xZmYq6YPnEpj6G0M/HcagL8YSlPg92G2Nylmbu/iy/4VJbEq5g/3PTcTtQDE9L/magX3eotNbG9Eqmv4yq3Uy4PZ4OF7J/XB7PQpKbVTNSKW8+w7MLx5EFje+jhSXF7Ny+8r6z6c6B46ymmK6XlPN5HWFnLm0kMBhFnb914tFsUGs/5cPJbsaFz5RnF4cVYMspTxQ+6v6SlVLaOhlJ2RA3JC1azfw55/LmTx5AqGhwWzZsoP09Ex69mw6s/fzz7+TkrKfsWNHERDgx7JlKykrK6dnz3gAHnnkP8yZ8x/8/Hw555xJWCwWNm/eTlZWFvfffzcAXbtG8ddfKxg3bjQmkwl/fz/uuedOrrjiegYP7s+kSRNYvPhPPvvsa7755iOn5o2Pj+Gzz75i+PDBVFRUcv/9j2I0trAOsuKo6B01L1otsXCVlpSahpa4WLSjBllJLBQdSKB5LB5hvzmeaDYipryHV5ddHPhhDkgNOxY0DFhFBbv8/kNI9WTiSu9DJz1YF3wRPpbehFU17ZEsTD3Qd34LGfJf7EVvYSt8DeuByQhTP7TAuWi+VyG0puV9Zp9Ikse9wP6RjxC24z0iN79Cv0UXU+kXQ8bAOWT3uQGb0auRVjlr7giy7hhG4Hd76TxvLdF3LibysRXkzBpI9m1DsIQ1ti8VHhrGWcEYbgrC+lsJNfNyMD+QifmpbIw3BGGcHYLWzbHOhtnjOuzSzqKVi5hx9gyEgNBxFkLHFVO6T0fCfA9SP3InZaE7YVPMdL+rktAJNS5vpFSc/Dgd+AohzhFC/CyE2C2EiKw9NlMIMbH9lqdoCb6+PqxatZapU6+ke/ch3HvvQzz00L+b3djm5+fLjz/+wuTJ0+jVazgvvTSfBQteZezYUQDMnDmDd9+dzyeffMnAgWMZN+5c3n33A7p27VI/xgsvPMnff/9Dly59GDzYsblu2rTzeOWV55g370369BnBq6++xWuv/Y8LLjjHqXnffXc+5eUVDB16JldffRPXX38NXbtGtuepO21pi0IhLaFeg2xxTYPsagZZCBPSrkpNH0+ac49w1VWio2kuMGpJwOTMOTjWfAHmkfhG72Tkq4MZ+tRkggb/TsaSG8jfPAUfH9BwfNvN9vgBoz2Q6LLZ+Fj64GmNxtMSS7nBsQfETvN3bYQ+CF3wQxjiDqDr/B5gx5Z1A5bErtjynkZamy+GazN6kzH4LtbelMiO87/C4h5C/LI7GbUgkpgV92MsO7RtqT5Y1msUXN6LHatuYMeyGZSOjSL8+dUMjn2N2Jt+wmN703cOhSYwnOeH59LueK7riWGqHzVv5lLecyeVVyRjXVdOcmZyo7ubNpuNpMykRuP5dLcx5LUypqbk0ffxcoq26vn7HH9+HxxA6kduRzrdKU5xhDMidyHENcBbwLvALUBvKWWKEOJfOOzfprTvMp1j8OBYuXbti02+lpgYQY8eMR28IsWpxN69ycTFnZobBHMPwMw4E3cssDDp+o4rP2XLKyc9/HEC5k3D57bRALz/fvMVwHyy1zHksxFsu+hnCqLPc3oea8Z07JWrMcantHrNdVTq0lkSEcWAggV0LZ/VZuN2FB1tu+YMt9zS/Gt1ThHO2q45086ZNs6cJ2fPZVue8/1eCzDZQvGrGYq7rXOj13Pd/mC33/8xJmcZeumJRZSxNXAWRnsg/QtfB8CGmWLTRgLMIxA0LymQUiIrlmLLfxFZsQSEO5rf9egC70KY4o+5Vp+sNURtfJHgpO+RQiO3+5WkDb6b8tCB9W3qbOLqnycVEvb6BkIWbkNXaaF4Yjey5gyjeHIMaM1/O7Fn1lDzei417+ZDsQ3dcE+Mc0LRT/ND6F37VmMzw4Ev3dg3z4OSnQbcQm3E3lJF3L8qMQW5YD2iOKG43nj9JinlkGO1czaDfB8wS0o5Fw772rkWGOD68hQKxYlEW23Sc5VDhUKc3aR34hQK0UnHWk5Wm7eOtl1rK5y1SnOmnTNtnDlPzp7LtjznXctvJqzqQtxtncnw+Jwk75cPe93D2hWBIM3zAyr0qez2+z8yPb4ivMJxJzHR+0XWhpzP9oDZ/BoRxAHPD5qdSwiB5jUZQ9fF6GN2oPleib34PSxJ3bGkXYi9YvlRdcqlnUeyc+o3rLkpicwBtxOU9APDPhnEwK/OJDD5Z5D2Rjrl6tgAUl+ewqaUOzjw1Jm478mj19QvGTBgASHvbUFUN33N0MKNuD0dgXdKX9zmRWLPt1J1dQrlvXZifjUHWebc3SoAnQmiZ1Rz9qZCxv1ShP8AKzsf92JRTDAbbvemdJ/SKZ/KOBsgxwFNWRaUAyf4DTKFQnEs6iQWHb5Jr94H2TUNsssuFu2wSU8oDbLiBMHLGl+fAbZRjUWU4GWNpU/Ry6R7fUSy98uker9OeOXlBJnPIMftd3b530tkxXTGHvyHoflfkuH5CdXasTdBa2590Ie/jyE+DS34YWTlKqz7x2NNGYKt+DOOZjhV7duNxDPnsfrmdJLOeB73oiT6/3ABwxf2ovO2t9EsjprQDQNla4A7mfeOYnPCbBIWTsXupiP21l8ZEjOfyCdWYMitaHIu4aXDeFsIXjt74/5VNFqEEfO/MyiL3kH1/RnY053/fysEhE2qYdxPxZyzJZ8uV1aT+pE7v/YLZMU0P3KWG1zyslacHDgbIGcBTd1HOQNIbrvlKBSK40Fb+SC7yqFNeu3tYtEOm/SUBllxguBXM5iYsjsBqNQfYKf/vZTp9xBoHsWonKV4WmPQS096F72AWctjj99DxJb+m6iK69BLL3xrBlJk2oBZ57xLkNCHog95AkN8OrqwBUh7JbbMa7AkdMOW/wLSVtxsX6ubH2lD72XNzBR2nfsZNqMXPf64hVELoui26mGMFQeBwwNladSRf01ftq+7iZ1LrqFsaGci//sPg2PmE/Ovn3Hfndf0OnUCwzR/PP/qjueqHuin+FDzSg7l3XdQOT0F28amA+zm8O1tY9jbpUxNzqP3gxUUbDCwbFIAS0YEsP9TN1z97q44cXE2QF4AvCqEGF37PFIIcR3wPOBisU2FQnGi0VYSC7vVTkW2mYy/Ckn5Lpf9P+VRsL2MqrymPzWEpoFecz6DXF9q+gSyeRNq547ixMHb2h299ObvsKFsDJzOik4jyXdbTp+il/GwRZLmtZAarYg+xYdEzyXGLQRWj0GTjg1+NswUGTeQ7vnpMecTmju6gFkYYnehj/oZYYrHlnMfloQIrNl3Imua1/1LnYGcnlex8ZoNbL78b0rCR9N17VOMeqcLPX+/Ac98RwW/hoEyQlA6vit7f7iCzTtuIXdGP4I+38XAAQvoecHn+P6R0qx2RjfUE49PovHa1xfj7BCsv5VQMWovFRP2YfmxGGlzPg3sFiLp+0gFFyTlMeT1UmyVgrU3+PJz9yD2vOBBTZGyvTjZcarUtJTyeSGEL7AUR3npZYAZ+J+U8vV2XF+bIqVssnCFQnEsnK3YdLKi04OmyVZlkM3FFlbcvpf9P+Wjd9cwBRiwlNuwVtoIGerD6BfjCejt1aifMOmRFic1yPq6SnouFueoLRTSltcADX29rZZCcSLRt+hFYkrncNBjEZEV0wkwj8IgHWrIZO959Ch5rL6tRZRRbNyEQIe7LYoy/V52BMzBrMtFSD27/O5jaP5XBJpHNzObAyE0hPd5aN7nYa/air3gJeyFb2IvfB3hPQ1d0D1oHqOa60xx5DiKI8fhXpRI5KZ5hO36gLBdH1DQZTLpQ+6msMvkRhZx1d0DSXn9XNIeH0+nBZvp9OZGep/7ORV9Q9j3xSVUxwU0OZ0WZcTt+UhMD3WmZmE+Na/lUnVZMlqsCeMdIRhmBCI8ndMX690hdlYVMTdVkb3YyN55Hmx70JtdT3vS7fpq4mdX4h3jvO5ZceLgVIAMIKV8UAjxFNALR+Z5t5SyvN1W1sYYDDaqq2twd2++RLNC0RzV1TUYDKf2RU5vbF0Gefm/9qCZNK7cORLvKLf645ZKG5v+m8qyWXuY9vdgdEeUohZGnQsa5JbavBlxFAS1Qq0NVlugSeNJm0H28WneUaE9aCsHByGad55wFWfGcqaNs+fSmXZtdZ48bFFEl80+7FipYScGux+B1eOQ2BFoFJnWkOf2F5EV12ITlST4PoMm3RmZ8xtu9k7s8J9LjtvvxwyQG6K5D0CL+AgZ+gy2wjewF72JNfU7hPtwtMC70XwuRoimw48q/zgSznqdlNFPEL59ARFb5jPg27MpD+xN+uC55PS8BrverVGwnPF/Y8i8ZwRBX+4i+NOdmCOP/YcsfHSY5oRivD0E6/dF1LySS/WcdKofy8Lten+8zzOi89dR2Tfk2GNp0PmcGjqfU0PRNj37XvEgeYE7iW+4E3Ghw085aKRF+SmfRBw1QBZCeAAvANNwfKr8Adwppcxv/6W1LYGBhWRmGggP74ybm1FlkhVOIaWkurqGzMwsgoIKj/dy2hWDqXUa5Iw/C7lqzyjcgw8v5mLw0DHi6Vje9VuGtcreKEDGqHPaxULWSSysLdAgg0OHLNowQMZ40mqQO9rKra0cHN5sQ1GfM2M543Th7Ll0pl17uot4W3rjYe1GhSERb2t3CkwryfD8HDdbGFEVM9jr+wR2YSa29B7c7I6y1b41g0j2fpkeJY867pq4gDCEow99Chn8f9iLFmIrfAVbxhXYDF3QBcxB85+J0DUuBAJgdQ/kwPAHSBtyD6F7Pydy08v0XDKTmJX/R8aA28nsfysWj2DAIcFwu/FDpElP3oz+5M3o79o69QLDZQEYLgvAuqYc8VQKPV7+Hf08G56mKsoHdSLhp0uxezuXYPPvb2XE+6X0f6qcxDfcSVrgQcYPbgQMtdDjrgoiLjKjuXYqFceBY/0TPQ5cD3wKVANX4dAcn9il5JrA29sM5JCVZcFiUdYsCucxGGwEBRXW/g2dujgyyC3/4ugZ7kbW8iK6nB+EVus3ardKbGZJ5p+F+MZ6NJk9EUa906WmD1XSa4EGGcBuBs3Ttb5H4WTOICtOLyQSgSDQPJYNQZcTXnklB90XEVlxLd3KbqVCn0yJcQtB1eMJMo+t75ft/gM+lr5o6Ouzzq4iNE90gbPRAm5Flv2EreAlbDl3Y8t7DM1/FrqAOxDGLk32lTojB3tfx8FeM/BP+4vITS8RvfpRuqx/hoO9ZpA+aC6VgT3qM8pH+im7irGvkT6566k6N5AE3+4ULbIycPVGPMf+Q+HTQ9Gf7YM4ig9zQ9zD7PR7soJe91eQ+ok7+17xYPU1fnhE2YifXUnMjVUYfE5t+d7JzLEC5IuBm6SUXwAIIT4BVgkhdFLKk+5+s7e3GW/v7OO9DIXihMRgAksrkqGjX47nrxt2kfDJQYIGemPw0mEps1KSXEXm30WMfbU7Rp/Glxxh0jtdahpNh13o0OwtsHmDdtioZzppM8iK0wuBI6iLL72fTlXnk+f2JxEVVxFSPQmAXLel1GhFhFadU9+n0LiWSv1+ehU/XTuG68HxYWsQOoTPNDSfadirNmLPfxF7wTzsBfPQfC51yC88hjXXmaIuEynqMhGPgj1Ebp5Hp90fEb59AfnR55E+aC5FURMaSS9cQkrCXt+AvriaxPWXAuBdZEVM3I1fSjaZ05LQ4k0Y7wrFcE0gwt2586H3hLh/VREzs4qsn03se9WDrfd5s/NJT2JurCJ+diWeXTquQJPCOY71rxsJ/FP3REq5HoeIr3HZHoVCcVKjN7ZOYhExIYBL1w2j83h/SlOqyF5ZTElyFf49PblkzVCiL2pax+fQIDuXQQaH1VurJBZtiCZNJ22hEMXpi4+lDzFlc+qDY3A4WVi0Irys8UgcWc1E3+cJqBmOt6Vnm69Bcx+CPvJzDPGpaIFzsZf/hjV1OJbUsdhLv+doObjKwJ7sm/Q2q2elkTLyMXwObmDgN2cx9ONBdNr1UX0hocPcL5zAkFtBp7c2ceDJMw8dkxbkUF+sD8fh/kFX8NRRfVsa5TE7qH4sC3uO85t0NR1EXGhm4p9FTF5TQPh5ZhJe8+DnHkGsutqXgg1Kd3EicawAWQeNrv5WXNjcp1AoTg70hta5WJSmVmEKNND/rigmftibc77vz1kf92Hw/3XDK8Kt2X7CqEc6m0HGIbMQLmeQ6wLkNs4goyQWilODwOozMNlCsIoKJBb2+D5KuX4vkeXX4mGLard5hSESfacXMMRnoOv0MtKSgTX9YixJ3bEVvIa0Ne8FYPEIZv+oR1k96wB7Jr+LsNfQ6/frGPVuN7qsewZ9lWPfiLOBcsiH27F5Gim4onf9Mc+tBzFmlWHp7IXh6kA81/bAY2k8uuGe1DyTTXnMdqpu3o9tZ5VL7ztgsJWRH5Vy/r58us+p5OBSI0tHB/LHeH/SvzdhP+nu0Z96HCtAFsAnQohFdQ8cNm/vHHFMoVCc5LQ2g/zjxE2UJjk+JKRdIuWhx9EQJh3S4kqAbHK5kp6olVjINs8gn7yb9Dqa5twxGh53pk1bzteR45yo89XhWzMQoz2I3yPCWRNyLpmeX9Kv6DUCaka278S1CJ03usC7MMQloo/4GqELwnbwDiwJkVhzHkBasprta9e7kd33JtZft5OtF/9GRWBvYlb+H6MXRBL/x+24FyUBNCpnfSTue/MpOj+u/rnpQAl+S1KQOo382qBZCIF+nDce38bguaM3huuDsHxZiGnQP1Scn4h1aalLtqCeUXYGPFvO1JR8Bv6vjKpsjVVX+PFL70ASXnPHUq4MBY4Xx8oENyXg+aQ9FqJQKI4veiNYalp+Mb503TDcAh0OEc5uYgHAhU164Ni006JKeuBSBtkZuy21Sa/tbMmgbZ012mqsjnb76Oj56tBhYmj+55QYtmHRSvG29MBkD67f3NdRCKFH+F6K5nsp9so12ApexJ7/PPb8/6H5XokWeA+a+4DmOlPY7WwKu52NZ952oja9TOcd7xC+7U3yY6aSPuRuisPHghBNbuorHROJ/++1xYFtdkIWbsVjdx7Zs4eCJsBmB11tXlET6OLdiBpWgruhkPA3NnBwRSbblvRD6+OOcU4IhisDECbndMoGb0n3OyuJu72SzB9M7H3Fg813+7DjCS9iZ1YRd1slHhFKp9yRHDVAllLe0FELUSgUxxeDCWytqHnhFmRA2mnyo1RKib1Gomviw0KYdMhy57Owdp2pXmPoNPWb9Jzv54zdliZNyNO8UIiztmTtaV+maDt8LYdbpLkaHOeZ/q4tZX0PYVVTEbTcNUrzGInm8Q2yJgVbwavYi9/DXvIJwvNMdIF3I7zORYimA9CK4H7sOXshyWOeJmLr64Rve5Pg5B8pDR1C+uC7yY2/FKkzHBYolw2PIPzFtfQb/h5WPzd0ZWay7h5J8eSY2pNx6FwE/LAX77WZeK/NIPc6xznLWzQRtzQPaublYp6VivmhTIy3hmC4ORgtyDllqqaDyEvMRF5iJn+dgX0ve7D3JQ/2zvMg6vJqus+pJGCg8wkFRctp3ZZUhUJxymAwta5QyI756ex4NY2assYXb0uZjT3vZVKR3XgCV2zewKFBdjmDrLWTi4XSICsUh2HVyqjWZ7I+5GKWdo4n2ftVrKJ1NcWEMRp92DwM8enoQp9HmhOxpl2AJakXtsK3kPbm9b81XmGkjPkvq25OZ9/EN9DVlNL716sZ+V4MURteQGcuARzyi6J1/2bNPWvJmTWQ7NuHsPebyyi4tHaDos0OmsB9dx5RDy8j4tlVlA/pzN5vLsN7dTrFk6MpHx+FcUYQnpt6MvCMFLq7J2J+LJPy6O1U3XYA275ql9530HALo78o4by9+cTdWknmIhNLhgfy51n+ZP5sRKqEcruiAmSFQgG0vpJe8re5eEW5YfTW12vw0pcWUHnQjNFHz94PsilNbfxBJgw6lzbpSc3Yggxye7lYKA2yQtGQsKoLOCszkaF5X+Nm68SOgDksDo9il9/9VOkyWjW20PmhC7oXQ3wKuojPEJoXtuxbsSREYc15GGk52Gxfu8GDzAG3su6GPWyb9hNVfjHErriP0W9HELtsLm4lqfVtD2ivkJ3/NJbO3gR9sYuwV9bVSyvibvoJv6Up7PzjWgou7Yn32gxCPtlB0oLz6/uHLtyKm7WaYO8iJvqvoNuAfCwfF1DRdxeV05Kw/l3mkk7Zq6udQS86dMoDni2jIlXHPxf782vfQJIWuGOtbMHJVBwTFSArFArA4WLRmgDZWm6r9zm2WxwX/1VzE8jbVAY4Nu5ZKxoHwsLkYgZZb+oQDbIzaNKITWWQFYrD0NATXnkpZ+Ss4ozsNQRXTyTR5wWWhHdjY+B0io2bWzW+EAZ0vlehj96AvutyhMdo7PlPYUnsgjXzRuzVO47SWaMg5ny2XL6M9dM3kR87jYitrzHyvVh6/3Q5Pllr65tWv38dJXtmIPWHQqX0B8cgdRp9Jn2C71+pdHlwGRn/GY0lzFERUF9QSciH28m5cQDbNs1i77eX0iU3kV63FGN6OAzbhgoqJydQMWwPNZ8WIGucTwMb/SQ97q7k/L35jPy4GIOPZONsHxZFB7P9UU+qc1RI15aos6lQKIDWl5p2DzVSdsBxC1Fn1JBSYq2218sqNINoevOeyflS01DnYtHCSnrt4IMslQ+yQtEsATUjGJb/NZMyk4kum81Bjx/5O2wwK0PPJNt9EZKW6wSEEGieZ2CI+gFD7D40v5nYS77AmtwPy/4p2MsXHzVTWx46iN3nfszqmftJG3IvAQeWMuTzkQz+bBTBCd+A3UZZlz7sd3+tvk/R+fHs/HsGudP7Ej/9B9wTCjh4y+D61702ZWPIryT0va3o8yooGxPF5r23k/XoGEwPd8YrsQ9ub3UBs6T6hv2Ux+/E/PxBZJHz10DNAF2uMDNpdSET/iokeHQNu5/1ZFFMEOtm+lC8QznxtgUdehaFELNxlK7uC3wupbz+KG3nAv8B3IFvgVulbOP0j0KhqEdvBKul5bvVYy4LZddbGVgrbQQP9qF4XwUmfz37Ps4m7bd8Anp74RPj3qifMB5eSe/GG3/k/fcvbHYeqRnRWSpcWlu9zZvd+UuIj0/z7gx1ODTIbRMg33orNPVZLgS8+WbHjwPOOVQ4c56cbefMfG3pmqHoODxtXelb9DI9ih9jv/cCUrznsy7kQrws8cSUziWyYgZ66dHi8YUpDn3n15EhT2Avehtb4XysB85GmPqgBc5F870aoTXtx17jHU7yGc+yf8RDhO1cSOTmefT96TKqfLuRPmgO2X1ubFShL/eGAUQ9upzyIZ0Jf2ktaY+cgd3LSOmoSLavuZHIx5fT58yPSfzoQioGhWH3ctzF0nSSgH41uP3HTnZALDWv5GB+KBPzM9kYrgvEdEcoWozJufcsIGSMhZAxJZQm6Eh8w4OUD9xJ/cid0LPM9JhTSafJNQ33FipcoKO/ZmQB/wWm4Ah8m0QIMQW4H5hQ2+d74PHaYwqFoh1orQ9yzxs6U1NqZcdr6dhqJOPf6sEFvw9i+6tpVOXVMPC+rvh0bSpAbqxBPlqQbNeb0FcXura4FmiQnQm22lKD3FyiywWpYpuOA845TzgblDrTzpn5lBvGyY1B+hJXei8xpXeR5fEtST7/Y1vgrez2e5Bu5bcSXTobN3unFo8v9IHogv8PLfAe7KVfYs9/EVvWTdhyHkAXcDtawG0IfVCTfW1GLzIG3UHGgNsISl5E1MYXiV92F91WP0pW35vJGHgHZp9Iqt+/js7/fEGNWxg7/rkGrbwGu3utvKw2EN7/4mRiyn7Gb2kKFYPCAPDYlkOXh/7CcLAC9Bpdsv8i4bOLKX4ugppXcrC8k4/lzTz0F/hhnBuKbpQnwsno1ifexuB5ZfR5pJzkd9xJfNOD5Rf449PTSve7Kuh6VTW65us1KZqgQyUWUsrvpJQ/AAXHaHod8J6UcpeUsgh4EkfmWaFQtBOtdbEA6D8nimsSRjNj/xiizg7CLdDAsMdjGPdGT3y6ujd5u9NlDbLWMT7IzqB8kBWKlqFhIKLySsYd3MCYgysIMp9Bgs/TLI6IYnPgDZQYjqIjdgKhmdD5zUAfsxV9lz8Q7kOw5T3qKDyS9S+kee9RFqcjP+4iNl+1kg1Xr6Ow69lEbnqJke92o9cvV+Ods4mssVey4f++p/r967B7GfFem4khy7HfQtQWPtIXVmGsPeaxM5ew19ZjN+rZ89OVbF9zIwWX9sJvcTK6/h64v98Nr8Q+GO/rhG1lGZVn7qNizF4sXxUirc5/uzUFSHr9p5LzE/IZ/l4JmlGy4V++LIoNYueTnlTnqnSys5yoGuTewLYGz7cBoUKIwCMbCiFuFkJsFEJszM9XKQSFoqUYTK0rNQ2OjXjmIgs560pI+T6X5G9zyF5ZRGlqFXarvclsiKs2b1JnQnO51HT7aZDtSoOsULQYgSDIPJbhed9zVtY+upbdTKbHVyzr3I9VIZPIcVuMpAW3P+rGFwLNayKGLr9giNmF5nct9uIPsST1xHLgfOzlfx1Vp1wWNoxd53/B2pnJZAyaQ1DKzwz9ZAgDvxyHf8afIO3UvHUFYXem0e28rWgVNUiDDr/FyQirnfLBjuxx0Je70KptZM0djqWTFwAVAzrh/1sSWB06bK2zEbcnw/FK7ovbq5FQZKNqeirlPXZinpeDLHHe7UdnhG7XVjNlfSHjfy8iYLCVnU968VNsMBtu86ZkT8v9qU8XTtQA2QsoafC87nfvIxtKKRdIKYdIKYcEBbVzLU6F4hRGbwBLK2O9Ha+n80XfNfw0eTNr7k9kzf1J/HrhNn4+dwtJX+RgtzXxQWTUgdXutO2RXWdEuFrRpD0DZHF6FwpRKNoKL2sc/YteY0pmOr2KnqHMsJs1oWfzV1gf9nu9iw3XfISPRLj1Qt95AYb4NHTBjyOrNmA9MBFrykBsxR8jj/LFu9qnC0njX2TVzekkjnsR95L99PvxQka8352wXe+x+4ZnsfgEMSjiHaJHb6f7JT9S2TeE4ikxuO/Jx31fAeXDOlM2Jqp+zIBF+6jsEwJ6DeyHrn/CU4fxlhA8d/bG/bsYtC5GzPdlUBa9nep707Hvd/6ulRDQaUIN434s5tzt+XS5por9n7jzW/8gll/ox8G/jC2SX50OnKgBcjnQMNqt+73sOKxFoTgtMBjB2gq1wM430kn5Npfx7/RiZsmZXLNvNNMTR3NTwXiGPRHD9lfTOfBLfqN+wlibyXDSC7llLhbtJLFQhUIUijbHaA8gvvR+JmemMij/AzSMbA2cxZKILuz1fRyzlteq8YU+BF3IIxjiD6Dr/C5IK7bMGVgSu2HLewZpbX6Pg83kS/qQu1kzM5md53+JxS2A7n/NZuTCWMzRGttnv0Z+/wlsuesDErp9QNkvt2PMLEVfWEXRlJj6cbzWZWI6UEL+lb0dB5pw+BGawHC+H55/dsdzbQ/05/lR81ou5T12Unl1Ctb1rm1W9ulhY9ibZVyQnEefR8op3KTn77P9WTwsgNSP3XDVXv5U50QNkHcBDetd9gdypJTH0i4rFIoWojeC3S6wtbCKafaqYiImBtDlnCBkg2yIlJLYy0LxiXancGfjilrC5Njc4qzMQrakkl5tgNzWRjiaNCKFFYnztz6bo7m9OK7uQG+rcaCxE8WxjrcWZ+br6DUpjh8aRqIqrmN89mZG5/yJn3kIe/0eY3F4FFsCbqZMv6dV4wvNDZ3/TehjdqCP+g1h6o0t9/8cOuXs2UhzUrN9paYnt/vlbLp6LZuu+IeiiPF0Wf8sg34YQ2D+19i9DoVXpnci0JLdqY4PrN8tG/6/NZQP60xlj6Y3DB6JbpAnHh91wyuhL8a7QrEuLaVyzF4qxu3F8n0Rsqm7c83gFizp81AFU5PyGfZOCfYawbqbfPkpNojdz3lgLlQ6Zeh4mzd97Zw6QCeEcAOsUsojPxk/Aj4QQnwKZAMPAR905FoVitMNQ60KwVoDuhZcGbwi3CjdX011oQWjrx67xQ52hy65OKGSmlIrXhGNt1G7GiDbdSaEiwGyEAKEoV0kFgB2LOhonabPVQu29h4HOt42zZn5lJXb6YdAEFw9geDqCZTp95DsM480z4844P0OoZXnElM2l+DqiQhaFtgJIRDeZ6N5n429egf2gpewF72DvfANhPeF6ALnIjzGNu0oIQQlEWMoiRiDe3EyEZtfIWzn+4Tt+pDCqImkD76b4tjBBOxZRc2bl2G66QsinlmJ+74CMu8ZQU2Ur0tr1SKNuD0bgenBMGo+LKBmfg5VV6Qgoo0YZ4divD4Q4eXctUjnBtHXVdNtRjUHlxrZ94oH2x/2ZtczXnSbUUX3Oyrxjmv9l/+TlY7OID8EVOGwa5te+/tDQogoIUS5ECIKQEr5O/A8sAw4UPt4tIPXqlCcVuhrVQgtdbLoe0ck1fk1fD92I+seTGL7vDS2vniANf9JZPHl2/GNdSf64uBG/eokFs6Wm7brjGgtuRcoTO3iYgEomYVC0UF4W3syoPBtpmSm0aP4cYpNG1kdOollYQNJ8/yo1ZtmNbe+6MMXYog7gBb0f8jKf7DuH4c1dTi2ki+Qsvk9B1V+MSROeJXVN6eTNPZZPAv30P/78+j59zXorYWMuX8s3YcsJ+DdTPad/SLlIyJavE7hrcM0OwSv3X1w/yIaLdSA+e50yrrtoPqBDOwZzp8HISBscg3jfynm7E0FRF1WTcr77vzSJ5B/LvYld6XhtNQpd7TN22NSSnHE4zEpZZqU0ktKmdag7UtSylAppY+U8gZVJEShaF8MJscVsKUb9bwi3JjyVT9GPBOLpcxG7oZSCneWo3PTMeG9Xox9tQcGryZS0y4GyA4XCwtIFytwCWP7ZZDbyAtZoVA4h8keTI+SR5ickcbA/PeRWNgcdB1LwruS4PMMNZqLXulHIAyd0If+17GhL+xNpK0EW8ZVWBJjsOX/D2krabav1c2ftGH/YfXMVHad+wl2gxs+4idkRCbVXTzZcdsrFPUYSfV7M6h+/7rDipC4vE6dwHCxP57Le+DxT3f0Z/lQ83IO5fE7qJyRim1LpUvj+fW1MvydUi5Iyqf3AxXkrTHy14QAlowMYP/nbthPoz3JJ6oGWaFQdDB1GeTWWL3pTBrdpgZzxus9mPJVPyZ91pdRz8cRNsa/2T7C6KrEwrFQ150s2iFARmWQFYrjiQ4TXSpuYEL2Tkbm/I63pQ+7/f+PxeERbAu4nXJ9QqvGF5oHuoBbMMTuQR+1CGGIxpZzL5aECKwH70bW7G+2r9QZyel5DRuu3czmy5dRHD2MzilvMvTzAfRYPBOPwkMaameC5IgnV+CzbH+zVX/0w73w+Dwar719MN4egvWXYiqG76HirH1Yfio+bG/IsXDvZKfvYxVMTc5jyGulWMsFa6/z5eceQex50YOa4lNfp6wKdisUCsBh8watKxZiq7GTtbyIjD8KqTxYg7RJjP56Qof6EnFWAJ6dG5dQrXexcDZA1mpLttrM2PTOlWR1TGQCF0pNO4OSWCgUJwYCQWj1FEKrp1Bi2EGyz0sc8HqXVK836VR1PrGl9xJoHtMKnbKG8L4AzfsC7FWbsBe8jL1gPvaCVxA+F6MLvAfNY0RznSmOHE9x5Hg8CvcRuellOu3+kM4736Og6xTShvyboqiJjcpZN0RXXE2nBZuJevIfKvqFkDVnOPlX9EYaG+uNta4m3F6IxPRQZ2rey6Pm9VyqLklGizVhnBOK4dpAhIdz+VG9B8TeXEXMzCqyfjWy71VPtj3gza6nPIm+vpr4Oyrw6ubi3byTBJVBVigUQMNNei37AKkptbL81r38MX0n1YUW/OI9COjrhaYXbHo6lWUzd1OS1Ph2X/0mPYvzEgvAdR1yu2iQ6zbpKYmFQnGi4Gvpy6CChUzOOED3kocoNK1mZaczWN5pKBken2OndToBzX0w+ohPMMSnogXdiyxfijV1JJaUUdhLv0XK5q9llQHd2TfpLVbPSidl9JN45W5l4DeTGPZRfzrt/ABR67VZJ72oC5ptfm5sSpxN0tvnISx24m76iUHxrxH+3Cr0hVVNziV8dZju7oTX3r64f9wN/HRU35FGecx2qh/JxJ7t/HkQGoSfX8OEJUVMWVdA+FQziW+580vPIFZd6Uv+WoMLZ/DkQAXICoUCONzFoiUkfXmQiiwzVyeM5sx3ejH4wW4M+k9Xxrzcnav3jsIr0o1tr6Q16ndok56TGeTarLFwsZqeEMajbrBpCUqDrFCcuLjZO9Gz5AkmZ6bRv+AtrFo5G4OvZml4NIk+L2ARzeuInUEYItCHPoshPh1dp1eR1hys6ZdiSYzDVvAK0tZ86QaLRxD7RzzE6lkH2D1lIQC9Ft/AqHe60HXtf9FXHXK1rQuSpZue3BsGsHXrzez++UqqegXT5eG/GRw9n25zfsctqWndtTAIDFcE4LmqBx7LuqMb7U3Ncwcpj9tB1cz92HY0HWA3h/9AKyM/KOWCxHx63F3Jwb+M/HFGAEvP8Cf9WxP2FlqFnmioAFmhUAANXCxaGOuZi60Y3DVMvk0rt9xDjNQUN75yHrJ5c9LFooHEwiWEsV0KhYCSWCgUJzJ66UG38n8xMWs3w3MX4WmNY5f/fSyOiGC7/xwq9KmtGl/ovNEF3oEhLgF95LcIQ2dsB+9y+CkfvBdpSW+2r9SbONjnetbP2MbWSxZTHjKA6FUPM3pBJPF/3Ip7oUNDfVhGWQiKJ8ew+9er2bppFgWX9iT0va0M7P0m3S/9Gu+VaU3qlIUQ6Ed74fFNDF67emO4KQjLN0VUDN5NxTkJWH4vcbqiKYBHuJ3+T5dzYWoeg+aVUp2rseoqP37pFcS++e5Yyk5unbIKkBUKBQB6Y62LRQtjvcB+3lTlW0j4JBtLpY3qQgtVeTVU5phJ+OwgOetKiJwc2LhjXQbZhUIhAJqrZf/aI0CuzSDbROtK4CoUivZHoBFWdQFjcv5ifPYmwiovItX7TZZ2jmV90GUUGte0bnyhQ/O5GEO3lei7rUXzmoK94GUsCdFYM67GXrXpaJ0p7DqZbZf8zrrrdpLT42rCdi5k5MLu9P1+Kn7pf9cHvQ2D5cq+ISS9ewGbkmaTcf9ofFam03fCx/QbtZCgL3YhmpGuabFuuL8ShXdKX0z/Dce+p5qqqUlUDNhNzcJ8ZLXzumK9J8TfVsV5uwoY83Ux7uE2ttzjw6JuQWy934uKtJMz1Dw5V61QKNqc1kosoqYE0m9OJGsfSubTmFX8ct4Wfpu2je9GbWDtA4l0uzCY7teGNcpQ1GWQcVZioWuZxMKhQVY2bwqFAvxqBjG44CMmZ6YSV/pv8tz+YEXYKJZ3Gkmmx9fYaZ1OQPMYjj7ySwxxSWiBd2Av+xlryhAsqeOwl/6IPIpNZUVQb/ZOeZfVsw6QOuIRfLPXMOirMxnyyRBCd3+CaLD/ok5+YenkRfrj49mUcgfJr52NrtRM/IwfGNTjDTq/tBZdcdNf4kWAHtN9nfBK6IPbwq5gFFT/6wDlMTswP5mFPc95WZqmg4gLzZy1rIhJqwsIm1LDvlc8+Ll7EKun+1K4+eTyhVABskKhAA4FyBZzy2+LxVwSyoz9Y5j65yCGPBzN4Ae7cfZ3/ZlxYCx9b49EStmoGlW9zZvThULqNum5mkFu+016uvoAWUksFIqTEXdbOL2Ln2NKZjr9Cudj1nLZEHw5f3SOJ8l7HhZR2qrxhbEr+k4vYYjPQBf6ItKyH2v6NCxJPbAVvoG0VzTb1+IZSurox1k9K429kxags1bS+7drGfluNFHrn0NfXQQcbhFn9zCQc/Ngtuy4hT3fXkZ1tD9d7/+TIdHz6XrPEkz7i5tZp4bxmkA81/fEY0k8uqGemJ/Mpjx6B1W3HsC2xzWdcuAQK6M+LeH8vfnE31lJ1m9GlowI5M8J/mQsMmE/CQr0qQBZoVAAh2zeWuODXEdALy+6nBtEl3ODCOrvDdBkcAwNNum5KrFw2cWi7X2QRZ3Nm3KxUChOavTSi+iy2UzKSmBY7ne428LZGTCXxRFR7PS7j0pd4w3GriB0PuiC7sYQl4wu4guEzh9b9u1YEqKw5jyItGQ129ducCer3yzWXb+LbRf9QmVAD2L/uZ9RCyKJ++tO3IuTG7leoAmKLohn19LpbFt3IwVT4+n05iYG9XiD+Cu/xWttRtPrFAL9eG88fojFc1svDDMCsXxaQEX/3VROTcT6Z6lLOmXPLnYGPlfO1JR8Br5QRkW6jpWX+vFr30AS33TH2vz3g+OOCpAVCgXQ+lLTx6Kp4BhakkE+cTbpqQyyQnFqIdDRueoixub8w7js9YRWnU2yz0ssDY9mQ9BVFBk3tm58oUfnewX6bmvRd1uJ8DgDe/4zWBK7Ys24Dnv1tqN01iiIPpetl/3B+mu3khd3CeHb3mLEe3H0WXQJvpmrQMpGwXLFwDCSPriQzQm3k3n3CPz+2k+/Mz6kzxkfEPjtHrA1LffQ9XTH/fUueKX0w/RoZ2ybK6k8J5GKIXuo+agAWeO8TtnoK+k+p5Lz9+Qz6tNiTAF2Ns3xYVF0MNse9KIq68QLR0+8FSkUiuNCXanptsggu4TJRZu3Og2yixlkoZmQbV5JT2mQFYpTFf+aoQzN/4JJmSnElN5FjvsvLA8byj+hZ5Dt/iOSlusEhBBoHqMxRH2PIS4Rzf8W7GXfYk0egGX/WdjLfjuqTrk8pD97zvmQ1bP2c2DY/finL2PwF2MY/NkIQvZ9haj1Wmsov6iJ8CHt6QlsTLmDlJcnY8ytoPtV3zGo15uEzV+PVtb0F30tSI/pwTC8kvritqAL2CXVM/dTHrcT8zPZ2Auc12treoi6zMyklUVM/LuQkPE17H3Rg5/iglh7ow9FW08cnbIKkBUKBdBgk17bWgUfk7oMMi5rkI+/xEJV0lMoTn08bFH0Kf4fUzLS6VP4EpX6A6wLmcYfnbuT4vU6VtE6nYAwxqAPe9XhpxzyLNK8B2vauViS+2Arehdpb17/W+PVmZSxT7Pq5nT2TXwdQ3UhfX6+ghHvxRK58SV05tJGGWW7l5GDtw9l865b2fvVJdSEedHtnqUMiZ5Pl/v/xJjetO5auGkYrw/Cc3MvPH6ORevjjvnRLMqjt1N1Rxq2BNfcfIJHWRjzZQnn7iogZlYVGd+bWDwskGVn+5H1q5GjfD/oEFSArFAogPaXWDTHIR9kZzXIJmw6ExylWlUzE7WDzZvSICsUpwsG6Uts2VwmZSYzNO9LjPYgtgfOZnF4BLv8HqBK17yO2BmEzh9d8H8wxKWiC/8YIdywZc1y6JRzH0Vac5vtazd4kjngNtbeuI/tF/6A2TuKuOX3MHpBBLF/341b6QHgCD9lnUbhtB7s/Ps6tq+8nuJJ0XR+ZR2D418j7tof8NzU9PsRQqCf7IvnL3F4bu6F4fIALAvzqei7i8qLk7CuKHNJp+wdY2PwvDKmpubT/6kySvfpWTHNn9/6B5L0jjtW1/YHthkqQFYoFMChALmlpaZbyqFKes4FvBVBvVl+VzX5cRe5OlE72rypDLJCcbqgoSe88nLOOLiGsQdXElw9kUSf51kS3pVNgTMoMRxFR+wEQjOi85uOPnoT+q7LEB4jsec94QiUM2ciq3cfrTP5sRey+coVbLhmA/nR5xOx+VVGvBtD75+vxDt7fX3ThsFy+bBwEj67mM17byf7jmH4/5pI/5EL6T3xY/x/SgB70wGvro877u90xSu5L8YHwrCtKafyrAQqRu7F8nkh0uJ8oGz0k/S8t5ILEvIZ8UEJOnfJxtt9+CkmmB1PeFKd07EhqwqQFQoF0NDmrXXjrHsoid8ucuEDQq+BEE5nkFuMMIG9fQqFqABZoTj9EAgCzaMZlv8Nk7IS6FZ2C1ke37Gs8wBWhkzkoPsvSFquExBCoHmOxxC1CEPsXjS/G7CXfIYluTeWA+dgL1961ExtWach7D7vM9bMTCV98N0E7P+doZ8NZ9DnYwhO/I6GXmt18gtzF1/2P38Wm1LvJPX5s3A7UEzPS75mYJ836fTWRrSKppMMWqgBt8c645XSD7c3oqDcRtV1qZR334H5xYPIJqqoNodmgK5XVzN5XSET/igkcJiFXf/1YlFMEOv/5UPJLp3TY7UGFSArFAqg7QLkiiwzhbvKnW4vhECYdB0QILdDBrm+1LSSWCgUpzOe1hj6Fb3KlMx0ehc9R4UhgbUh5/NXWB9Svd7GJlqnExCm7ug7v4khPg1dyJPI6i1YD0zGmtwfW9FC5FG+/Jt9Ikke9zyrb04nYfzLmMoz6bvoEkYs7E7E5vnoahzX64YZZZuPiey7hrNp7+3s+/QirP7uRN+5mMHR84l6aBmGrLKm1+muYZwZjOf23rh/H4MW64b5gUzKuu2g+u507CnOf8AIASFnWDjjh2LO3ZlP9A1VHPjCjd8GBvH3+X5kLzU2VVG7zVABskLRBLm5y9m4cRarVl3Exo2zyM1dfryX1O5oGmg62WoXC82oYTO7mDUx6pHNlERtM4QRsB51Z7jLQ6IhpF5lkBUKBQBGuz9xpfcxKTOFwfkfo0l3tgXewuLwKPb4Pka1ltOq8YU+CF3wQxjiDqDr/D4gsWXdiCWxK7a8p5DWgmb72ozeZAy+i7U3JbLjgq+xuIcQv+xORi2IJGbF/ZjKDnkj17tf6DUKLuvFjpXXs+PvGZSO60L4C6sZHPcasTcuwmNb0+9HaALDeX54LonHc11PDNP8qHk7j/JeO6m8IhnrWueTKAA+8TaGzC9jakoefZ8oo3i7nuXn+fP7oABSPnTDVddPZ1ABskJxBLm5y0lOfgOzOQ+QmM15JCe/cVoEyQZT610sdEaBvca1r/XCqHPaxaKlCFGbIm8HJwu1SU+hUDREw0BkxXTGH9zImIN/E2AeyT6/x1kS0YUtATMpNexs1fhCM6HzvwF9zHb0XZYg3Ppjy30IS0Ik1qzbkOZ9zfaVmp68+EvZdPVqNl61hqIuZxG18QVGvtuNXr9OxytnC3DEhj4hKBsVyb6vLmXz7tvImTWIwO/3MmDou/Q6+1P8fktqXqc80AP3hd3wSuiD8Z5OWJeVUXnGPirG7MXyTRHS6vznhSlQ0vv+Si5IzGf4uyUgYP0sX36KDWLnU56Y89tuD40KkBWKI0hL+wT7Eber7HYzaWmfHKcVdRx6Y+slFi3JIAuTvmMkFtAOThYmbCqDrFAomkAgCDKPY0TeIs7K3EdU+Q1keH7GX537sjrkHHLdliBpuU5ACIHmNQlDl9/Rx+xE870ae/F7WJJ6YEmbir1i2VF1yqWdR7Dzgq9Zc1MSGQNmE5T0I8M+GcTAr84kMPkn6rzWGvopm2P8SZ03hY0pd3DgqTNx31dArwu/ZMCABYS8twWtquksixZuxO2pcLxT+uL2SiT2AitVV6dQ3msn5ldzkGXOJ0l0Jug2o5qzNxUy7pci/Ada2fm4F4tigtlwuzel+1qvU1YBskJxBGZzvkvHTyUMJrCYW/cNXGfUsLlQYQlwaJDbOYNMu2WQTUpioVAojomXNZ4BhW8yJTOdnkX/pcS4hdWhU/grrC8HPD/ARuuuI5pbb/Th72KIT0MLfhhZuRrr/glYUwZjK/4UKZu/PVjt242kM19m9c3pJJ7xAu5FSfT/YSrDF/ak87a30CyVjfyUbf7uZN47is37bidh4VTsbjpib/2VwbGvEfnECgy5TftDCy8dxltD8NrZG/evotEijJj/nUFZt+1U/ycDe5rz12ghIGxSDeMWFXPOlny6XFlN6kfu/NovkBXT/MhZbmixTlkFyArFEZhMQS4dP5VoiwyyzqRhr5Eu+WAKQ0dmkNt+o57apKdQKJzFaA+ke+mDTM44wKD8DxHo2BJ0A0siurDX90nMWuuSMUIfij7kCUfhkbAFSHsVtszpWBK6Yct7Dmkrbrav1c2P9KH/Zs3MFHad+xk2ow89/riVUQuiiF75EMaKg8Dh8gtp1JF/TV+2r7uJnUunUzYsnMj//sPgmPnE/Otn3HflNb1OncAwzR/Pv7rjuboH+im+1LyaQ3n3HVROT8G20bUCLL69bQx7u5SpyXn0frCCgg0Glk0KYMmIAFI/ccPV2lIqQFYojiAqajqaZjrsmKaZiIqafpxW1HEYTG2xSc+Rgba74H+J0bUMsrBbMVYcxD/tL4ITvyMw+Sc883ZgqDzKB0t7BcjSqDLICoXCZXSYiKqYwZnZWxmVswTfmoHs9XuExeGRbA24hXJ9QqvGF5o7uoBZGGJ3oY/6BWHqji33fiwJEViz70TWpDTbV+oM5PS8io3XrGfTFSsoCR9Dl3VPM+qdLvT8/QY883bUt62XXwhB6bgu7P3+cjbvuIXcGf0I+mIXAwcuoOf5n+P7RwrNpXN1Qzzx+DQar319Md4ZivX3EipG7aViwj4sPxYjbc5/nriFSPo+UsEFSXkMeaMUW5Vg3Y2+/Nw9iD0veDg9TocWvRZCBADvAZOBfOABKeVnTbS7vrZdQ1+U86WUf3fAMhWnOSEh4wCHFtlszsdkCiIqanr98Tpyc5cfs83Jht5AqwNkndHxvdteY6///VgIkx5qnMsg66uL6f7HLQQl/4hd747FLQBdTTk6ayWlnYaReOYrVAT1bmKS9gqQTWqTnkKhaDECQUj1JEKqJ1Fq2EWy9zzSvD5gv/fbhFaeR2zpPQSZxyNomfxNCA3hfS6a97nYq7ZiL3gZe9Fb2AtfQ3hPQxf0bzSPUc11piRiLDsixuJelETk5nmE7VxI2K4PKOwyibTBd1PYdcphGmW3Gz+kunsgKa+fS9rj4+m0YDOd3txI73M/p6JPCFl3DSP/it5IU+MQVIsy4vZcBKaHwqhZmE/N/FyqLktGxJgw3RmCYUYgwtM5fbHeHWJnVhFzYxXZi43snefBtge9nT9vrtwGbS1CiM9xZK1vAgYAvwCjpJS7jmh3PTBTSjnGlfEHD46Va9e+2DaLVSiOQp3TRcPNfJpmIibmtpM6SL5rmIHAzpKHf2i53GHHa+msujuB67PPwC3Q4FSf7DPfQBg0Oi25pf7Y++9f2GTbPosuxa4zkTz2Gcw+UfXHNUsl3dY8gX/6X2y6ciVSZzysn730W6zpl6KP2Ybm1q8F76xplnUajJstjJF5P7fZmAqF4vSmWsthv/dbpHq/gVmXi695IDFlc4mouKLef701SEsWtsLXsBe9DbZChPtwtMC5aD6XIMTRc6f6qkLCt79NxJb5mCqyKQ/sTfrgueT0vAa73u2wtm43fgiAMFsJ+nIXneetx3NnLjWdPDl4yxAO3jwIa1DzWV1plVh/KKZmXg629RXgr8M4KxjjrcFo4a6fh6JteuYOnb5JSjnkWG07TGIhhPAELgEellKWSylXAouAaztqDQpFW3GqOl0YTGBpZalpncnR3xUnC+GCxCLgwFISz5x3WHAMYDd4kHzGs3jm70KzNmHKX79Jr41dLJQGWaFQtDFu9lB6lDzK5IwDDCh4G7uoZnPQDJaEdyPB5zlqtKJWjS8MndGHPu0oPNLpNaStAFvGlVgSY7Hlv4y0lTbb1+oewIHhD7B61n52n/0hUtPTc8lMRr3Tha5rnsBQeUhzXJdZliY9eTP6s23TTHb9ehUV/UOJemw5g2PmEz37N9wSmvZvFnqB4VJ/PFf2wGN5d/Tjval54SDlcTuouiEV27ZKl963f38XKvq5NHLriAdsUsqGopptQBP3QgEYKITIF0IkCCEeFs18pRFC3CyE2CiE2Jif3/w/qELRlpyqThd6Y+slFlqtrMIVJwtXAuRq7wj80v9Gs1Yj7FaE3YpmrUZnLiE44Vsq/eOgqVuR7SmxUAGyQqFoB3S40bX8ZiZk72Jkzq94W3qy2/9+FodHss3/Dsr1Sa0aX2ie6AJvxxC7D33kDwhDFLacux065YP3IGsONNtX6owc7D2DDdduYctlf1IaOoTo1Y8y6p0oui/9Fx4FewAOc75ACErOimbPT1exZcvN5F/Zm5APtzGoz1v0uOgrfJYfaFanrB/phceXMXjt6YPxlhAsPxRTMXQPFZMTsPxagmzGh7mldKQG2QsoOeJYCdCUIGQF0Ac4gCOA/hKwAs8c2VBKuQBYAA6JRRuuV6FoFpMpqLaQSOPjJzMGE1Q1XUHUaTRDrQbZFS9ko/MuFolnvkqv366lbPdHlIUMwmb0QldThntxEv5pf5Fw1hvYTD6NO9ZlkI9SkrUlaNKIVWvlSVMoFIqjIBCEVp9DaPU5lBi2keTzEvu93ybV+3XCKi8itmwuAebRrdMp+1yI5nMh9qqN2Atewl7wCvaCV9B8LnXILzyGN9eZoqgJFEVNwKNgD5Gb59Fp90eEb19AfrdzSR98N0VRE+qD5DrZRVXvYJLfPp+0J8bT6a1NdHp7M30mfUL5gFCy5gyn4PJeSENjvbEWbcLtpUhMD4dR834+Na/nUjUtCS3ehHFOKIbpgQj31ud/OzKDXA4c+anlAzT6ZJFSpkgpU6WUdinlDuAJ4NIOWKNC4RSnqtOFwSjbwOatVmLhQjU9VwqFFHWZyIZrN1MUeSbuJcn4ZvyDe3ESlYG92Dh9I3lxFzc3ieNnOxQKsbfSv1ShUCicxdfSn8EFHzIl8wDxpQ+Q77aMfzqNZXmn4WR4fImd1llmau5D0Ed8hiE+FS1wLvby37CmjsCSOgZ76fdI2fzdvsrAnuyb9DarZ6WRMupxfHI2MvCbsxj68UA67foIYatp5KdsCfUi/dFxbEqeTfIb56BVWYm/YRGD4l8n/IXV6IqakMwBwl+P6Z5OeO3ri/sHXcFTR/XtaZTH7KD60UzsOa0rC9uRGeQEQC+EiJNSJtYe6w/sOkqfOiRN3jNVnC60pWPEjh2PUFq6vf65j08/+vZ9wqX5QkLGUVq6h5ycJYAd0AgOPrPFazpRHDHaQmKhM9VmkC2uSSywOCexcCtJxewVQfqQu11bWLvavCmJhUKh6FjcbGH0Kn6K+JL/I93zI5J8XmZj8JW4W6OIKZ1Dl/KbMEjfFo8vDJHoO72ADH4Ee/H72ArmYU2/GIwx6ALmoPndgNB5NdnX4hHM/pGPkDb0PkL3fEbkppfo9ft1xPxzPxkDZ5PZ7xas7gGHZZXt7gZyZg4i58aB+C1OpvMr6+jy4DIinl5J7vX9yZo9DHOMfxPrFBiuDkR/VQC2f8qpmZdDzbMHqXkpB8NVARjvDEXXx93l999hGWQpZQXwHfCEEMJTCDEauBD4+Mi2QohzhBChtb/3AB4GfuyotSpOLOocIxySBonZnEdy8hvk5i53eawjg2OA0tLt7NjxiEvz5eYuJy9vGY7gGMBOXt6yFq2pLd9fa3Fs0mvdGHXWbi5v0nMygzzoizNwL67V3Um7Q69W9/OokzgyyLJdNumpDLJCoTg+6KUn3cpv5aysvQzP/REPa1d2BtzD4ogIdvjfTaWueR2xMwidN7rAORjiEtFHfoPQhWA7eCeWhEisOfcjLZnN9rXr3cjueyPrr9vB1kt+pyKoDzErH2T0gkji/7gd9yJHvvQwnbImKD4nlt2/X8PWDTMpuKgHoQs2M6jXG3S//Bu8V6c3eb0XQqA/wxuP72Lx3NEbw/VBWL4spGLQbirOT8S6tNSlAlYdXSjkNsAdyAU+B26VUu4SQkQJIcqFEHXb0icC24UQFcCvOALrpzt4rYoThLZ0jDgyOG7quDPzteWaTiRHDEclvdbdrKkrFOJSgOyCxGLDtZup9I+v7ag5ao3W/TzaHPUZ5HaQWKgAWaFQHGcEGmFVUxmbs5zx2RvpVDWVFO9XWRoew/qgyyk0rmvd+EKP5nMJhujV6LutRnidhT3/BSwJXbFmTMdeteVonSnsOoWtly5h3Yzt5HS/gs4732XE+93p+8M0/DJWgJSN5BeV/UNJen8qmxJnk3nvKHyWH6Dv+I/oO/YDAr/eDdamP2d08W64z4/CO7Ufpsc7Y99eSeV5iVQM2u30++3QAFlKWSilnCal9JRSRtUVCZFSpkkpvaSUabXP/y2lDK1tFy2lfEQerYi44pSmox0jnJmvLdd0IjliGExtKLFwVYPspCTD4hEMmg6kHc1S5SgSYi5BsxzD7qdeg9y2cgidNGFHXZ4UCsWJg1/NYIbkf8qkzFRiS+8h130JK8JGsCJ0DFnu3yFxvnJpU2geIzFEfo0hLgktYDb2sh+xpgzCknom9rKfkbL563lFcF/2nv0+q2cdYP+IB/HNXMmgL8cx5NNhhO75HGFzXE8bBsuWzt6k/fdMNqXcQcqrU9AXVtH9mu8Z3ON1wuatQ1fadJJCBOgxPRCGV2Jf3N7tCprzCSBValpxwtOcM0R7OUY4M19brqmj39/RMJjaYpOe6xILDM5LLADcSg/QZf1z9PnpUgZ+OY5ev82g2+rH8MlaC/ZmLvxa+2zSE6rUtEKhOEHxsEXSu/g5pmSk07dwHtW6LNaHXMLSzvEke7+KVZS3anxh7IY+7GUM8enoQp9H1iRhTbsAS1JPbIVvIe1Nb7ADqPHsROroJ1l9cxp7z3oTXU0pvX+9mpHvxRC14QV05kPGZ3UZZbunkYO3DGHLjlvY882lVHfxo9t9fzC426t0ve8PTAeONEurXadJwzgjEM+NPZ1+bypAVpzwtKVjhI9P0xXUGh53Zr62XNOJ5IjRJj7Ihpb5IFNjc0of5pWzmYFfTSA48Tusbv64lWcgpB1jVS59F11E2M6FDk1y40kcP9t6k54qFKJQKE5wDNKbmLI5nJWVwNC8b3CzhbIjYA6LwyPZ5fcfqnQZrRpf6PzQBd2LIT4FXcTnCM0HW/attTrlh5CW7Gb72g0eZPW/hXU37GHbtJ+o8oshdsV9jH47gthlc3ErSQUOzyij0yia2p1df17LtjU3UHRuHGHz1zOox+vEX/M9Xhua1kWLY0jxGqICZMUJT0jIOGJibsNkCgYEJlNwi0s69+37RKMg+UgXC2fma8s1teVYrcVgpPUZ5FoNsqsSC6RsVk/WkJiVD5Ix4DY2Tt/A7nM/Yd11O0DaSR31OJuuXEXnne/inbO5iUnaJ0DWKQ2yQqE4SdDQE155CWfkrOaM7NUEV08i0ed/LAnvxsbA6RQbN7VqfCEM6HyvRB+9Hn3X5QiPsdjzn8aS2BVr5g3Yq3ccpbNGQcz5bLl8GeunbyI/dhoRW19j5Hux9PnpMnyy1tQ3rd/QB1QM7kzix9PYlDCbrDnD8VuSTL/RH9DnzI8I+GEv2Fy4m9mAjrR5UyhaTGnpHszmAhwuDwWUlu5pFEA6Y98GEBo6EbM5u95SLTR0YqM2ISHjOjRA7ej5mkNvBLtNYLOBrrE/u1NophZmkAFptiKaMIZviKG6gCrfGMcTKbF4hGCszMUrZwv5cdPQWSoxVjSRrWinQiFCGpHCisSOUDkHhUJxkhBQM5Jh+SOp1B0g2WceB7zeJcPrU4KqxxNTOpdOVee3+JomhEB4noHmeQbSnISt4GXsxQuxF3+A8JyELvBuhNeUZjO65aGD2H3uxySNfZaIra8Rvu0tQhK+oSRsBGmD7yY/7qLDgmS3Gz+kJtKHA89OJP3BMYR8uJ3Or66jx+XfUh3tR9Ydw8i9rj92L6PT70FdzRUnPElJb5GT8zsNLdVycn4nKemt+jbO2LdB21mqnUjWbG2JoTaGtLYihmyJBlmYHN/VnSk3XRQxjuCk7+rLmIbteB+b0ZtqH4cJjsUtAETjINtRrV5rc5s3nXScNDtKZqFQKE4+PGxd6Fv0MlMyMuhd+D8q9MmsC7mQPzv3JNXrTayiolXjC1Ms+s6vY4jPQBfyNNK8E2vaOViT+2Ireg9pr262b413OCljn2H1zensmzAfY2UufX++nBHvxRGx+RV0NY5acw2dL+zeJg7OHsrm3bex7/OLqQnxJHruEoZEzyfq//5yet0qQFac8DiKcRz9uDP2bdB2lmonkjVbW1IXILfGC7nOB9kViQV1GeSaY2/USx39JCAY8ukwxr4RSMzKB8gYcBvloYMwVOaR0+MqKgJ6NN1ZGNtcYiGkIyOhdMgKheJkxiB9iSu7h0mZyQzJ+xy93ZttgbexODyS3X4PUa0dbNX4Qh+ALvgBDHH70YV/COiwZc3EkhCFLfcJpDWv2b42oxeZA2ez5sYEtk/9DrN3BPHL7mL02xHELL8XU2k6cISfsl6j4JKe7FxxPdtXXEfxhK6Ev7TW6fUqiYXiJKC5TKTruqK2slQ7kazZ2hK90RHUtmaj3qFS065nkDEfO4Ns17ux55wPSTxzHoaqAqr8oh0+yDgs4LL6/+toE7W5i4WO2gyyqHHU/FQoFIqTGA0DEZVXEl55BYWmVST5vESCz9Mk+jxPRMXVxJbeja+l6Q3vziA0Izq/GWi+1yIrlmEreAlb3qPY8p9B87sWXeBchKkZtwlNR37cReTHXYR39nqiNr1E5KaXidz0Mnnxl5E25B7KOg1pJL8oHxFBwhcRmFKLoftdTq1TBciKkwCNpoNh12+AmExBtbKIxsePxzgnGvpaeVZrNuppLamkZzikQXYKaQcEenMRwUk/gN2G2Sscs3cENZ5hSJ2hmYmM7VAopC6DrDbqKRSKUweBINA8hsC8MZTrE0n2fpU0r/dJ9/qQ4KqziC29h5DqKQhaVlxKCIHwmoDmNQFp3lOrU/4Ye9E7CK9z0QXeg/A8s1mdclnYMHad/wVupQeI2PwqnXe8Q+i+LygOH+vQKcdcAJrusHLW5m5+Tq9PSSwUJzyhoZOPedwZ+zZoO0u1E8marS0x1AbItlbUvdAMLXSxAKTFOfP6iC3zGfF+PIO+HEfs3/cQu+JeBnx3NgO/nkDovi+a90IWpra3eZMNMsgKhUJxCuJljaN/0XymZKbTq+gZygy7WRN6Dn+F9Wa/1zvYaF5H7AzC1BN95wUY4tPQBT+OrNqI9cBErCkDsRV/hLQ3f32t9ulC0vgXWXVzBonjXsRUlka/RRcxYmEPwre8jmZxaKgPk184gcogK1pEbu5y0tI+qXeCiIqa3mIXBscmvCU4ssQaoaGTiY29pf712NhbyM39BykPbRQQwvOwNn37PsGqVdMajX2ki0VIyDgSE1897Jjdbm209nXrbsRqLax/rtcHMHz4+4eNU1q657B1Bwef2eJz0JbnszUcyiALWqoXEEKgGYVrGWQXNMjhW14jZN/X7Dn7Awqizz3stZB9X9Fl/bNYjT7kx17YuLPW9hKL+gwyKoOsUChObYz2AOJL7ye29G4yPL8k2ftltgbezB6/h+hadivRZbdhsoe0eHyhD0YX8gha0H3YSz7FXvAytszrsOU8gC7gdjT/WxD6gCb72kw+pA+5m4xBdxKU+D1RG/9H979mE736YTL73ULGwNnUeHV2ei0qg6xwmbZ0cHDGoWLTpjsOC44BpKxg06Y76p+vWnVJk+MfeXzVqsuhUYlNW+1xB0cGxwBWayHr1t1Y/zw3dzl5ecsOW3de3rIWnYMTyRGjLkBui3LTrmiQqcsgOyGx8MtcSWGXSY7guGFBECnJ7X45VX4xeOU347UpjMi23qSH2qSnUChOLzSMRFVcy/iDmxid8yd+5qHs83ucxRFRbAmYRZl+T6vGF5obOv+b0MfsQB/1G8LUB1vug47CI9mzkeakZvtKTU9e98vYdPVaNl25kqLIM+my4TlGvdOVnr85n0FWAbLCZdrSwcEZh4rq6vQm2xx+vLlb80ceby6IOXT8yOC4qeNteQ5OJEeMtnCxAIeThWsZ5LoA+dgSC7NXBO6lqeirCkFKhM2CsJrRrNV45W5Dby6h2juy6XmUBlmhUCjaDIEguHoCI/N+ZmLmHqLKryPd8xP+DO/FmuDzyHVbimzF7mUhBJr32Ri6LkYfsx3N93LsRe9gSYrHkjYNe8WK5iuwCkFJ+Gh2Tv2WNTcmktn/FoITv3V6bhUgK1ymbR0c2s6hoiNpy3NwIjliGEytd7EAR7EQ1zTItb7FTkgs0gffhaEyj8GfjyTmnweI3PQSXTa+QOzyf9N30UVU+sWRF9f0HYX20CDrlAZZoVAo8Lb2YEDh20zJTKdH8eMUmzayOnQyy8IGkub5EbZWytA0t77owxdiiDuAFvQgsnIl1v3jsKYOx1byOVI2v3mm2i+axAmvsvrmphNuTc7XqtUqTkuac2pomYNDc3+CJ/afZlueg7Y9n62jLVwswFFuukUZZCcKhZi9I9gx9TuSz3gefU0pPgfX45m3A7vejd1nf0jCWa9jM3o1M5GpXSrpgcogKxQKBYDJHkSPkkeYnJHGwPz3kVjZHHQdS8K7ss/nKWq0glaNLwyd0Ic+6djQF/YW0laCLeNqLIkx2PL/h7QVN9vX6ubv9DwndhSiOCFpSwcHZxwq3Nyavl1++PHmyhMfeby5MpOHjuub2QDQ8HhbnoMTyRHjkAa5ZbY9deiMGnZXfJBdtHmTehP5sReyb9Jb7Jz6Lbsu+JKk8S9SEjH2GBO1faEQVUlPoVAoGqPDRJeKG5iQvYNROYvxtfRnj/9DLA6PZFvA7ZTrE1o1vtA80AX8C0PsHvRRPyEMMdhy7q3VKd+FrElt1fgqQFa4TEjIOGJibsNkCgYEJlMwMTG3NXJdyM1dzsaNs1i16iI2bpzV5Kaz2NhbCA09m0N/ihqhoWcf5lAxePD8RkGym1skgwfPr38+enTTuqIjj48e/RU08mwUtccdDB/+fqMguSkXC2fOgTO05VitxdBGGWTNRQ3yoU16ztm8CVsNAfuXEPv3v+n163R6/3wV8X/cRqddH2IszzpKx3ZwsUBlkBUKhaI5BIKQ6smMyv2dCVk7CK+8kgNe7/JHeHfWBk8l37SilTplDc37fAzdlqGP3oTmfSH2wtexJMZiSb8Ue+WaFo2rbN4ULSIkZNxRA7g6Z4a6zWd1zgx1fRsSG3vLYQFxUzQMhpuioevFkccbju1od+R/RNmoXcNguDmOdQ5coS3Hag2GNnOxENgsLfFBPnYGWWcuJX7ZnQQlLyIvZhqV/t2Rmh5jRTbd1jxBpz2fsm/iG1T5xzY1kfJBVigUiuOEj6UPgwrep1fR06R6v0Gq9xus7DQOX/MgYkvvIbzyMjSaKfTkBJr7ILSIT5Chz2ErnI+98G2spd8i3Ec4Co/4XOT8WC1ehUJxFDramcEZNwxX2p2u1EssWlEoBBw2by5JLGp9kLEcu0/o3s8xlWWyemYqe89+n/0jH+bA8AdInPAqa2YmU+0dReSml5qepx1s3g75ILfypCkUCsVpgpu9Ez1LnmByZhoDCt7GplWyKfgaloZHk+jzAjWiuFXjC0M4+tBnMcSno+s0H2nLw5pxGZbEOKfHUAGyol3oeGcGZ90wTk7XjI6izsWitTZvrkosRBM+yDfe+GOTbfXmYmwGD2wm3yZfr/EMRW8ubmaitrd5U5v0FAqFomXopQddy29mYtYuRuT+hKclnl3+97EkIpLt/nOo0LdORyx0XugCZ2OI3Yc+8luEQRUKURxnOt6ZwVk3jJPTNaOjaDMXC1dt3ozOb9IrD+6PsTKPTrs/RrNUoq8qxFCZh6Eih9A9n+KbtYbCrmc3M1E7SCxUoRCFQqFoFQKNTlXnMyb3T8ZnbSas8iJSvd9kaedY1gddSoFpVevGFzo0n4sxdFvpdB+lQVa0C1FR0w/TIEP7OjOEhk6urcjX+HhL2p2uHF5quuXoDK7ZvOFCgFzY7Wx0lnLil80hdtlcqn27IYWGqSIbYbdyYNgDHOw9A6QEccT7UIVCFAqF4oTGzzKQwQUf0av4GVK857PfawFZnt/ibx5BbOlcwiovRuuA8FUFyIp2oW7DWVraJ5jN+ZhMQURFTW+3jWh1G+wcWmI7DjeMyY02/znb7nSlrpJeWxQKcc0HuTZAdsIHGSAv/lLy4i/Fo2A37iWOW3BmrwjKQ/o7GjQVHDsW1g4Bstqkp1AoFG2Nuy2c3sXP0r3kYdI8PyDJ5yU2BF+Bh7Ur0aVz6FJ+Iwbp027zd2iALIQIAN4DJgP5wANSys+aaTsX+A/gDnwL3CplG3+yKdqVjnZmcMYNw5V2pyP6tnKxMGrYXNmkp2mg18BJH+Q6KgN7URnY6/CDzQXHoHyQFQqF4iRDLz2JLr+dbuW3kO3+E8k+L7EzYC57/R6la9nNRJfNxsPWpc3n7Wjh5etADRAKXAO8KYTofWQjIcQU4H5gItAViAYe77hlKhSnJzo9CCHbxObNFQ0yODbqSYtzGeSjD3QUeUitBlnKlntuNhqy1pJISSwUCoWi/RDo6Fw1jbE5KxiXvZ7QqnNI9nmZJeHRbAi6kiLjxjadr8MCZCGEJ3AJ8LCUslxKuRJYBFzbRPPrgPeklLuklEXAk8D1HbVWheJ0RQiIGyLxDWldAOndzR3/np4u9TEOikDXybtV8x4LYYhEuA0BXMtUH3VMBH7moZhsoW02pkKhUCiax79mKEPzv2BSZgqxpXeT4/4b/3QaQ41W1GZziLbMpBx1IiEGAqullO4Njv0bGCelvOCIttuAp6WUX9Y+DwLygCApZcERbW8Gbq592gfY2X7vQtEEQTjkMoqOQ53zjked845HnfOOR53zjked846nu5TymNmYjtQgewElRxwrAZpa5JFt6373Bg4LkKWUC4AFAEKIjVLKIW2yWoVTqHPe8ahz3vGoc97xqHPe8ahz3vGoc97xCCGc0mJ0pAa5HDhyu6EPUOZE27rfm2qrUCgUCoVCoVC0GR0ZICcAeiFEwzp//YFdTbTdVftaw3Y5R8orFAqFQqFQKBSKtqbDAmQpZQXwHfCEEMJTCDEauBD4uInmHwE3CSF6CSH8gYeAD5yYZkFbrVfhNOqcdzzqnHc86px3POqcdzzqnHc86px3PE6d8w7bpAf1PsjvA5NwaInvl1J+JoSIAnYDvaSUabVt7+ZwH+RblA+yQqFQKBQKhaK96dAAWaFQKBQKhUKhONHp6EIhCoVCoVAoFArFCY0KkBUKhUKhUCgUigacEgGyECJACPG9EKJCCHFACHH18V7TqY4QYrYQYqMQwiyE+OB4r+dURwhhEkK8V/v3XSaE2CKEOOd4r+tURwjxiRAiWwhRKoRIEELMPN5rOl0QQsQJIaqFEJ8c77Wc6ggh/q491+W1j33He02nA0KIK4UQe2pjl2QhxNjjvaZTlQZ/23UPmxBi/tH6dGShkPbkdaAGCAUGAL8IIbZJKZuykFO0DVnAf4EpODZSKtoXPZAOjAPSgHOBr4QQfaWU+4/nwk5xngFuklKahRA9gL+FEFuklJuO98JOA14HNhzvRZxGzJZSvnu8F3G6IISYBDwHXAGsB8KO74pObaSUXnW/CyE8gRzg66P1OekzyLVv9BLgYSlluZRyJbAIuPb4ruzURkr5nZTyB46obKhoH6SUFVLKx6SU+6WUdinlz0AqMPh4r+1URkq5q4F7jqx9xBzHJZ0WCCGuBIqBP4/zUhSK9uJx4Akp5draa3qmlDLzeC/qNOFSIBf452iNTvoAGYgHbFLKhAbHtgG9j9N6FIp2RwgRiuNvX90laWeEEG8IISqBvUA28OtxXtIpjRDCB3gCuOd4r+U04xkhRL4QYpUQYvzxXsypjBBCBwwBgoUQSUKIDCHEa0IIdTe2Y7gO+Egew8btVAiQvYCSI46VAN7HYS0KRbsjhDAAnwIfSin3Hu/1nOpIKW/DcT0Zi6PYkfJjb1+eBN6TUqYf74WcRvwHiAbCcRRR+EkIoe6UtB+hgAFHJnMsDmnoQBxF0RTtSG3djXHAh8dqeyoEyOWAzxHHfICy47AWhaJdEUJoOKpP1gCzj/NyThuklLZa+VYEcOvxXs+pihBiAHAW8PJxXspphZRynZSyTEppllJ+CKzCsc9B0T5U1f6cL6XMllLmAy+hznlHMANYKaVMPVbDU2GTXgKgF0LESSkTa4/1R916VpxiCCEE8B6O7MO5UkrLcV7S6YgepUFuT8YDXYE0x587XoBOCNFLSjnoOK7rdEMC4ngv4lRFSlkkhMjAcZ4VHcsM4FlnGp70GWQpZQWO255PCCE8hRCjgQtxZNkU7YQQQi+EcAN0OD7A3IQQp8IXrhOZN4GewAVSyqpjNVa0DiFESK0Nk5cQQieEmAJcBfx1vNd2CrMAxxeQAbWPt4BfcLjlKNoBIYSfEGJK3TVcCHENcAaw+Hiv7RRnIXBH7XXGH7gL+Pn4LunURggxCoeM6KjuFXWcKgHNbcD7OHYlFgC3Kou3duch4NEGz6fj2JX72HFZzSmOEKIL8C8c+teDtdk1gH9JKT89bgs7tZE45BRv4UgmHADuklL+eFxXdQojpawEKuueCyHKgWopZd7xW9UpjwGHZWcPwIZjM+o0KaXyQm5fngSCcNwFrwa+Ap46ris69bkO+E5K6ZQEVxxjE59CoVAoFAqFQnFacdJLLBQKhUKhUCgUirZEBcgKhUKhUCgUCkUDVICsUCgUCoVCoVA0QAXICoVCoVAoFApFA1SArFAoFAqFQqFQNEAFyAqFQqFQKBQKRQNUgKxQKBQnGUKI/UKIfx/l9etrPYRPCIQQHwghVBEEhUJx0qACZIVCoWgBtUGfrH1YhBApQoj/CSE8nezftbbvkPZea0dxKr4nhUJxenKqVNJTKBSK48EfwLU4qpGNBd4FPHFU4FMoFArFSYrKICsUCkXLMUspD0op06WUnwGfAtMAhIP7hBDJQogqIcQOIcT0Bn1Ta39uqM26/l3bb6gQYokQIl8IUSqEWCmEGNnahQohLhBCbBJCVAshUoUQTwkhjA1e3y+EeEgI8XbtvBlCiHuPGCNeCLG8dox9QohzhRDlQojrj/aeGvSfI4TIFEIUCSEWCiE8Wvu+FAqFoj1QAbJCoVC0HVU4sskA/wVuAm4HegHPAG8LIc6rfX1Y7c+zgTDg4trn3sDHODLSw4CtwK9CiKCWLkoIMQVH8P4a0Bu4EbgUePqIpnOBHcAg4Dng+brgXAihAd8DVmAEcD3wKGBq0L+590Tt++kDnAVcAVwEzGnpe1IoFIr2REksFAqFog0QQgwDrgb+rNUh3w1MllL+U9sktbbN7cAvQF7t8QIp5cG6caSUfx0x7h3AJTiCzk9auLwHgReklAtrnycLIf4DfCKEuFdKKWuPL5FSvlb7+3whxJ3ARGANMAnoXvueMmvXNhdY1WCeJt9TLaXArVJKK7BHCPF17djPtPA9KRQKRbuhAmSFQqFoOWfXukXocWSOfwTuwJExdgN+F0LIBu0NwP6jDSiECAGeBM4EQgEd4A5EtWKdg4FhtUFxHVrtuJ2A7Npj24/olwWE1P7eA8iqC45r2QDYnVzD7trguOHYw53sq1AoFB2KCpAVCoWi5awAbgYsOIJHC4AQolvt6xcAaUf0sRxjzA9xBMZzcQTTZuBPwHiUPsdCAx4Hvm7itbwGvx+5NskhKZ6ofd5Sjja2QqFQnFCoAFmhUChaTqWUMqmJ47txBLZdjpRMNKCm9qfuiONjgDullL8ACCFCceh5W8NmoEcza3WWPUC4EKKzlDKr9tgQDg9ym3tPCoVCcVKhAmSFQqFoY6SUZUKI/wH/E0IIHJlmLxyb2+xSygVALo5NfVOEEPuBaillCZAATBdCrMNhGfc8hwLPlvIE8LMQ4gDwFY6Ndn2AYVLK+5wcYymwD/iwtkiJO/BS7Vh1meXm3pNCoVCcVKjbWwqFQtE+PAw8Bvwb2IUjwLyEWiu0Wj3uncBMHHrcH2v73YgjmN4EfAG8zzF0y8dCSrkYOA+Hrnl97eN+Gss/jjaGHYfzhKm2/4fAUziC4+pjvCeFQqE4qRCHNi8rFAqFQuE8Qoj+OGzohkgpNx3n5SgUCkWboQJkhUKhUDiFEOIioAJIBLrikFgIYKBUHyYKheIUQmmQFQqFQuEs3jgKiEQCRcDfwFwVHCsUilMNlUFWKBQKhUKhUCgaoDbpKRQKhUKhUCgUDVABskKhUCgUCoVC0QAVICsUCoVCoVAoFA1QAbJCoVAoFAqFQtEAFSArFAqFQqFQKBQN+H/KuQDGI28e6AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "\n",
    "y_proba = softmax_reg.predict_proba(X_new)\n",
    "y_predict = softmax_reg.predict(X_new)\n",
    "\n",
    "zz1 = y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"center left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "save_fig(\"softmax_regression_contour_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict([[5, 2]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.38014896e-07, 5.74929995e-02, 9.42506362e-01]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "softmax_reg.predict_proba([[5, 2]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. to 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "See appendix A."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12. Batch Gradient Descent with early stopping for Softmax Regression\n",
    "(without using Scikit-Learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by loading the data. We will just reuse the Iris dataset we loaded earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris[\"data\"][:, (2, 3)]  # petal length, petal width\n",
    "y = iris[\"target\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to add the bias term for every instance ($x_0 = 1$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_with_bias = np.c_[np.ones([len(X), 1]), X]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's set the random seed so the output of this exercise solution is reproducible:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(2042)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The easiest option to split the dataset into a training set, a validation set and a test set would be to use Scikit-Learn's `train_test_split()` function, but the point of this exercise is to try understand the algorithms by implementing them manually. So here is one possible implementation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_ratio = 0.2\n",
    "validation_ratio = 0.2\n",
    "total_size = len(X_with_bias)\n",
    "\n",
    "test_size = int(total_size * test_ratio)\n",
    "validation_size = int(total_size * validation_ratio)\n",
    "train_size = total_size - test_size - validation_size\n",
    "\n",
    "rnd_indices = np.random.permutation(total_size)\n",
    "\n",
    "X_train = X_with_bias[rnd_indices[:train_size]]\n",
    "y_train = y[rnd_indices[:train_size]]\n",
    "X_valid = X_with_bias[rnd_indices[train_size:-test_size]]\n",
    "y_valid = y[rnd_indices[train_size:-test_size]]\n",
    "X_test = X_with_bias[rnd_indices[-test_size:]]\n",
    "y_test = y[rnd_indices[-test_size:]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The targets are currently class indices (0, 1 or 2), but we need target class probabilities to train the Softmax Regression model. Each instance will have target class probabilities equal to 0.0 for all classes except for the target class which will have a probability of 1.0 (in other words, the vector of class probabilities for ay given instance is a one-hot vector). Let's write a small function to convert the vector of class indices into a matrix containing a one-hot vector for each instance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def to_one_hot(y):\n",
    "    n_classes = y.max() + 1\n",
    "    m = len(y)\n",
    "    Y_one_hot = np.zeros((m, n_classes))\n",
    "    Y_one_hot[np.arange(m), y] = 1\n",
    "    return Y_one_hot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's test this function on the first 10 instances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 1, 1, 0, 1, 1, 1, 0])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [1., 0., 0.]])"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "to_one_hot(y_train[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looks good, so let's create the target class probabilities matrix for the training set and the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_train_one_hot = to_one_hot(y_train)\n",
    "Y_valid_one_hot = to_one_hot(y_valid)\n",
    "Y_test_one_hot = to_one_hot(y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's implement the Softmax function. Recall that it is defined by the following equation:\n",
    "\n",
    "$\\sigma\\left(\\mathbf{s}(\\mathbf{x})\\right)_k = \\dfrac{\\exp\\left(s_k(\\mathbf{x})\\right)}{\\sum\\limits_{j=1}^{K}{\\exp\\left(s_j(\\mathbf{x})\\right)}}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(logits):\n",
    "    exps = np.exp(logits)\n",
    "    exp_sums = np.sum(exps, axis=1, keepdims=True)\n",
    "    return exps / exp_sums"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are almost ready to start training. Let's define the number of inputs and outputs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_inputs = X_train.shape[1] # == 3 (2 features plus the bias term)\n",
    "n_outputs = len(np.unique(y_train))   # == 3 (3 iris classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now here comes the hardest part: training! Theoretically, it's simple: it's just a matter of translating the math equations into Python code. But in practice, it can be quite tricky: in particular, it's easy to mix up the order of the terms, or the indices. You can even end up with code that looks like it's working but is actually not computing exactly the right thing. When unsure, you should write down the shape of each term in the equation and make sure the corresponding terms in your code match closely. It can also help to evaluate each term independently and print them out. The good news it that you won't have to do this everyday, since all this is well implemented by Scikit-Learn, but it will help you understand what's going on under the hood.\n",
    "\n",
    "So the equations we will need are the cost function:\n",
    "\n",
    "$J(\\mathbf{\\Theta}) =\n",
    "- \\dfrac{1}{m}\\sum\\limits_{i=1}^{m}\\sum\\limits_{k=1}^{K}{y_k^{(i)}\\log\\left(\\hat{p}_k^{(i)}\\right)}$\n",
    "\n",
    "And the equation for the gradients:\n",
    "\n",
    "$\\nabla_{\\mathbf{\\theta}^{(k)}} \\, J(\\mathbf{\\Theta}) = \\dfrac{1}{m} \\sum\\limits_{i=1}^{m}{ \\left ( \\hat{p}^{(i)}_k - y_k^{(i)} \\right ) \\mathbf{x}^{(i)}}$\n",
    "\n",
    "Note that $\\log\\left(\\hat{p}_k^{(i)}\\right)$ may not be computable if $\\hat{p}_k^{(i)} = 0$. So we will add a tiny value $\\epsilon$ to $\\log\\left(\\hat{p}_k^{(i)}\\right)$ to avoid getting `nan` values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 5.446205811872683\n",
      "500 0.8350062641405651\n",
      "1000 0.6878801447192402\n",
      "1500 0.6012379137693314\n",
      "2000 0.5444496861981872\n",
      "2500 0.5038530181431525\n",
      "3000 0.47292289721922487\n",
      "3500 0.44824244188957774\n",
      "4000 0.4278651093928793\n",
      "4500 0.41060071429187134\n",
      "5000 0.3956780375390374\n"
     ]
    }
   ],
   "source": [
    "eta = 0.01\n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    if iteration % 500 == 0:\n",
    "        loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "        print(iteration, loss)\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    gradients = 1/m * X_train.T.dot(error)\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And that's it! The Softmax model is trained. Let's look at the model parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.32094157, -0.6501102 , -2.99979416],\n",
       "       [-1.1718465 ,  0.11706172,  0.10507543],\n",
       "       [-0.70224261, -0.09527802,  1.4786383 ]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Theta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's make predictions for the validation set and check the accuracy score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9666666666666667"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, this model looks pretty good. For the sake of the exercise, let's add a bit of $\\ell_2$ regularization. The following training code is similar to the one above, but the loss now has an additional $\\ell_2$ penalty, and the gradients have the proper additional term (note that we don't regularize the first element of `Theta` since this corresponds to the bias term). Also, let's try increasing the learning rate `eta`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 6.629842469083912\n",
      "500 0.5339667976629505\n",
      "1000 0.5036400750148942\n",
      "1500 0.49468910594603216\n",
      "2000 0.4912968418075476\n",
      "2500 0.48989924700933296\n",
      "3000 0.4892990598451198\n",
      "3500 0.4890351244397859\n",
      "4000 0.4889173621830818\n",
      "4500 0.4888643337449303\n",
      "5000 0.4888403120738818\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1\n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "alpha = 0.1  # regularization hyperparameter\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    if iteration % 500 == 0:\n",
    "        xentropy_loss = -np.mean(np.sum(Y_train_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "        l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "        loss = xentropy_loss + alpha * l2_loss\n",
    "        print(iteration, loss)\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the additional $\\ell_2$ penalty, the loss seems greater than earlier, but perhaps this model will perform better? Let's find out:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cool, perfect accuracy! We probably just got lucky with this validation set, but still, it's pleasant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's add early stopping. For this we just need to measure the loss on the validation set at every iteration and stop when the error starts growing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 4.7096017363419875\n",
      "500 0.5739711987633519\n",
      "1000 0.5435638529109128\n",
      "1500 0.5355752782580262\n",
      "2000 0.5331959249285545\n",
      "2500 0.5325946767399382\n",
      "2765 0.5325460966791898\n",
      "2766 0.5325460971327978 early stopping!\n"
     ]
    }
   ],
   "source": [
    "eta = 0.1 \n",
    "n_iterations = 5001\n",
    "m = len(X_train)\n",
    "epsilon = 1e-7\n",
    "alpha = 0.1  # regularization hyperparameter\n",
    "best_loss = np.infty\n",
    "\n",
    "Theta = np.random.randn(n_inputs, n_outputs)\n",
    "\n",
    "for iteration in range(n_iterations):\n",
    "    logits = X_train.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    error = Y_proba - Y_train_one_hot\n",
    "    gradients = 1/m * X_train.T.dot(error) + np.r_[np.zeros([1, n_outputs]), alpha * Theta[1:]]\n",
    "    Theta = Theta - eta * gradients\n",
    "\n",
    "    logits = X_valid.dot(Theta)\n",
    "    Y_proba = softmax(logits)\n",
    "    xentropy_loss = -np.mean(np.sum(Y_valid_one_hot * np.log(Y_proba + epsilon), axis=1))\n",
    "    l2_loss = 1/2 * np.sum(np.square(Theta[1:]))\n",
    "    loss = xentropy_loss + alpha * l2_loss\n",
    "    if iteration % 500 == 0:\n",
    "        print(iteration, loss)\n",
    "    if loss < best_loss:\n",
    "        best_loss = loss\n",
    "    else:\n",
    "        print(iteration - 1, best_loss)\n",
    "        print(iteration, loss, \"early stopping!\")\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_valid.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_valid)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still perfect, but faster."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the model's predictions on the whole dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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D+bkNgfBkF2ctPUpMTwd/XB3F5udDA+nr4RGCDlstOVB4kOnrvkCVKtPXfe7RKJsQEBohqy3vsWTJH6xfv4l582by88/fn/L8wYPZXHXVdYwZcyWbNq3i99/nMnp05cuqo0ePYt68heTl/espLl68nAMHsrniiksqPe/zz2cipWTx4nlMn/42mZl7ufTSMQwbdg5r1y7l9ttv4uGHnzh2vCFMV2FkzWaz8dxzr/DBB2+yfPkC8vLyueWWeyudd/78X7jootGcddYgVq/+jV9//YGBA/uilkXF7HYHTzzxMGvXLuWHH77kyJEjjB59faXjHU9lBXQ1zXFvadBpqz2+ctoAjp5zGv98/zSF3ZJp89THpN7+WsA1kj94S082z70Sw4FC0vpOI2LJnupPaoAIo4L53QRMk5vj/PIoJUO3oR4OzBInvsIUKxn8Uy7xl5eyfkI4q28JRw2+pcfQbnNHjfL00hdQywrHuKTK00te4M1hL3psfEskFOWBrQRMoRUfYzab+PDDNzGZKg4b799/EIfDwSWXjCQhIR6ATp06VDrnueeeSUREON9++wPXXXcNAF98MZMhQwbStGnlLWhat47nxRefPvb40UefIikpkRdffBohBO3aJbN9+w4mTCg7RggMoeX3CP/eOjmdTt544wXatUsG4N57b+e6625HVVUU5dR7imeeeYFLLhnJ5MkTju1LS+t07O/x468+9ndSUiJvvfUSHTv2Yt++LFq2bFHp6wFAp0OYDciiBrKcI4SWK6U0GKwfXev1HqTlOBpHs/nd+2j22c8kvDKTLhdNYMcz15PXP80n8/uC/CGt2bBsHKkXf02HoV+w+/Vzyb6+u7/N8jhCCEwPNUNJMlE6PoPiAVsJ/b4tunbBorB1RWeGMz4uICzRxebnwijZq6PvjHwMEcELXTDCVgvKo2t2lzv6YnfZPR5ls0S6AyZVLYt26tS+UmcNoEuXTpx55iDS0vpy6aVjePvtDzl8OKfS4/V6PaNGXcSMGTMBd8Rr1qwfGD36sipt7d696wmP09O307NntxOiaKeffmKLNL3FnW91fHkPk8l0zFkDaN68GQ6H44SI3/GsXbuBIUMGVmrX33+v48ILr6J1685ERrbi9NOHAJCZua/K11OOCDOWlfbQ/gVC6BSkq+HUjdMyvlKQAqAoHBhzLuu/egJHTAQdbn6Z1lM+Q9gaUGS3GqzJMWxYNpb8MxNpc+tPJN67EJyBuWxouCyG0F9SoMBF8YB0nIuDCtL6IBRIm1zM6e/lk/2bkV8GRVOcGXRXgu9ALTg+ulZOeZTNUyh6MIdV3fUgNLSS0FsZOp2OBQtmMX/+t6SldWTatM9o164H69ZVLrkfPXoUixcvJytrP3PnLsRud3DRRSOqnMdiOdEOKWW1YgJDmcNmL/xXKafXnxjoLR9DrUPif3FxMeeddwmhoSF8/PE7rFr1K/PmuR1Ru71msXUlzAQuFVnaAGLxOh04XcGkZw/iyyXSkpRWrP9qIvuvPptmn/9C2hWTCNkROPXMXJFmtnx/OfvvOp3mb66m/QVfocsLzBpm+l7HKUiHbcf+SVBBWl+SxloZ+GMeJZk6fu4fw9G1/+1FwaDDVgtW7Ft9LLpWjt1l5499f3p0Hk80gxdCcMYZpzNx4kOsWrWI5s2b8fXX31V6fK9ePWnTpjVffvktX3wxkwsuGEZYWO2q57dvn8KaNSeW31i9+q8T7dK7P3KOwrpHhbp168yiRYsrfC49fTs5OUd45pmJDBjQl9TUFA4dqjy6WBEizB29lA2ggK4wlF3AnP++n8E8tvrjS6dNmoxkPDKaze/ci+FIAWmjnqTpF78EjiBBp5DxwtnseHc4kb9n0LnfdMzbj/rbKq+gtDZhWdoOXf8wrNcHFaSeoOmZds78/SiKARYNiSZrrjZ7gvuCoMNWC/6+cQmux3NP2f6+cYlH5znWDD6vbuevXLmaZ555kdWr/yYzcy8//PATe/dm0b59uyrPu+qqy/jww0+ZN28ho0ePqvW8N900jp07d/PAA4+zdet2Zs36kffemw64U62Ox1HsQqp1u5A98sh9fPPNbB5//Gk2b05n06YtvPrqVEpKSoiPb4nJZOKtt95n164M5s5dwBNPTKnV+MKoQxh0qA0gj02Y3BcvWcPoYZCa40unDSCvfxrrZk2m4LRUkp75jNQ7XkefGzhLa4fGdWXTgtEYjpaS1ncakb/u9rdJXkFE6Qn94TgF6ZjdQQVpPYnq5OLspUcJb+di2SVRbJsa4m+T/ELQYdMgx5rB59etVUdkZATLl69k5MgraNeuJw88MIEJE+7n6qurLsA7evQotm7dTmRkBGefPbjW8yYkxDNz5sf8+ONPdOvWn9dem8rjjz8EgNl8YhKulOCoYzP4YcPO4dtvP2X+/F/o0WMggweP4LfflqIoCo0axTFt2lRmz55Lp069mTz5+ROEETVDuOuxNQCl6DGHzap957Ih4munzREXyZa372H3Q1cStWwDXS5+nIiVm31qgzcp7BfP+uXjsLUIp8OIGTR9e42/TfIKxxSkT7fA+VVuUEHqAUKaqZz561GaD7fx990R/H1fWGD23q4CEUjh2h492sqVK1+q8Lnt21uSmtrGxxbVnSP7Ie+goHUXidKA66K+/vo7PPHEFI4cyfhX8SklOeuKMMfoCYvX5p2SeqgQ5748jJ2bQdmyY3r6TpKTayZc8BWF3/3KkQlv0GLBuxha/qvo/eijC/xoVeDhKwXp8YRu2UPKA28TkpFN1g3D2XvrhUhDYOTw6ApsJI/5nph5Ozh4U3d2v3wO0tCAL3RV4Pgml9LxuxHNDYTOTg4qSOuJ6oJ/Hghn25uhtBhp5YyP89E34FbKY41j/5JS9qz+yGCETbM01GbwU6e+z59//sXu3XuYMeMbnn76Ba699qoTy3MIgTFCh73AiVaVmCLcncemFmo7yqaEui/+sqT0hP3BPDbP4lMFaRkl7RNY//VTHLq4Py3fm0Ona/+HKeuwT23wFq4IE+nfXkbWvb1p+u7ftD//S3S5pdWf2AAxXBpN6M8pUKgGFaQeQNFB95cL6f5yAVk/mlh0dgzW7P+GK/PfeJUNkPo2g/cXO3bs5pJLrqFjx1488cQUbrppHM8/P+mU44yRelx2iatUm7kdDaURvAh1RyjV4sBU3mkNXzttaqiJnZPGs/WFmwnZuZ8ul0wkdsFqn9rgNXQKe549k+0fjCBiaSZpfadj3hqYyspjCtImQQWpp0i5vZT+3+STv1nPwn4x5G8OzAjt8fjUYRNCfCaEOCCEKBBCbBNCVFp+XghxjxDioBAiXwjxkRDiP9dcrKJm8Frn5ZensHfvZkpKDrJt299MnjwBo/FUVY8xwr20Y69jHpv3EShhRtRCbTtsSri7tIpaVOJnS/47+NppAzgyrDfrvp1EaWIz2t37FklPTUexajv6W1MOj+nCpp+vRp9vJa3fNCJ/2eVvk7yC0vq4HqRBBalHaHG+jTN/PYpqg18GxnBwUWArSH0dYfsfkCiljABGAk8LIXqcfJAQ4lzgYeBMIBFIAp7yoZ2awBJV+2bwDQXFoKAPUbDla9Vhc5f3kFYHaLgwrRLmTt5QC4v9bMl/C384bbaWjdj46aNkjTuPpl//TucrJhGys2Y9crVOYZ9WrP9jPLZWkXQ4/0uaTg2QKOJJiCg9oXOSgwpSDxLTw8nZS48S2kJl8Ygodn0SuDmCPnXYpJSbpJTlIQtZtlWkBLgW+LDs+FxgMjDWN1Zqh5Dw6pvBN2SMkXqcRS6kS5t3mUpZPTYt9xVVIoIOm7/wh9MmDXr23H85m9+5F+ORfNIuf5LG3y0NiJpttoRINiweQ+55bUm6eyFJd/yEcGj3ZqmuCIM4VUGao90b14aAJUHlzMVHaTzQzp/XR7L+CUsgfCVOwec5bEKIqUKIEiAdOADMq+CwjsC64x6vA5oIIWIrGO9GIcQaIcSanJzAaqJc02bwDRVjhB7JiV0PtISwGEAITfcVVSLdxY3VvFPDsEHhgffxh9MG7ppt/8yaTFHnNrSd8CFtH3kPJQDyGNVwE+kzLyXrvjOOiRH0RwNPjCCEwPRgU0I+b43rrxKK+6fj2trw///8iTFSMvCHPJLGlbL5f2GsHBuBS7uX7jrhc4dNSnkrEA70B2YBFb2lYcDxcaXyv8MrGO89KWVPKWXPuLgIT5vrdyxR4HS4m8EHGoYwHYpOYNfqsqhQEBZt57EpJiMixFyhwxbEN/hDQQrgaBTFpg8eIPO2i2g0dyVdRj1J6Na9PrfD4+gU9vxvyDExQud+gStGMFwW41aQlvcgXRL8HtcHxQCnvVNA50mF7JkRwu/DorEdDZyAh19UolJKl5RyGdASuKWCQ4qA472v8r//c5/mY83g8/xtiTfQfnkPJcyELHG4kwk1ihIdjisvsKLLDRG/RNt0CvtuvYBNHz6IrthK2hVP0eTr3wJiifQEMUL/6QHbGUHf+7gepOdtx/5ZYDqnvkII6PhwCWd8ks+RVQZ+6R9D4c7AUJD6u6yHnopz2DYBXY573AXIllL+5z7Jiq6sGXwdux5oHWOkHtUhcZZo0yFSwk2A1HRfUV1MFK4jFSc6jh8/O7g06kP8tURacHp71n07ifzTUmnz1MckP/AOSnHDX0os7NPqhM4ITd79q/qTGiAnKEjHZ2B9KqggrS8JV1gZvCAX2xGFX/rHkLPS4G+T6o3PHDYhRGMhxBVCiDAhhK5MCXolsKiCwz8BrhNCdBBCRAMTgOm+slVrlDeDd1SxMjdkyAjuuOMB3xnlIdr37MnUT9/1WHkPT78PwmIEhKaXRXWxkahH8vxtRpAy/OW0OWIj2PLOvey5+1LiFvxJl8ueJHTLHr/Y4klsiVFsXHwtuee2oc0d82l913xwavMGrz6IaD2hP7bFcG0s9mcOUHptBtIWeK/TlzTq6+CsJUcxRKosOjuazG8adnUwX0bYJO7lz31ALvAicLeUcrYQIl4IUSSEiAeQUs4Hngd+A/aUbU/40FbNMG7crVw93t0DtCq16DfffMqUKRN9ZJXnWLVqETeMGafdPDZFQYQaNN0IXhcXhSvosGkKfzltKApZN4xg07SHUUptpF01OSCWSI91RrinF83e/ov2F3yFLi/wkvSFUcH8XgKmSc1xfnmUkqHbgwrSehKR4m4cH9PDwR9XRbHlxdAG+3XwmcMmpTwspRwopYySUkZIKTtLKd8vey5TShkmpcw87viXpZRNyo4dd1w5EL/RvHkEOl3UKVvz5t4VOwgBphAqVIva7e6lupiYaMLDT9Fk+BWHo/pmx40axRHVNBxHsQupgbtmVVVxnVR3TQk3uZdENfol18VG4zqaj9Rwvbj/In5z2oCCnu3cS6Q9y5ZIH3q34S+R6hT2PHcWO94bTuTvGW4xwvaj/rbK4wghMD3cjJDPWuNaU0zJgHRc2wPPOfUlpjjJ4Pm5xF9mZd2j4ay5LRy1AfrB/s5ha1BkV9KvrLL9nsQSKbEWwdixt3L++Zfz/POvEh/fkfj4jsCpS4GzZv1I1659sViaERfXmsGDh5OdfajCsa+66jouvXTMCftUVSUhoSOvvjoVACklL7zwGsnJ3bBYmtGlSx8+++yrY8dnZGSi00UzY8Y3nHXWSCyWZrz33jTy8/MZM+YmmjZNJjS0KW3bduW1194+dl5SUhpvTn8HcHc9KCgo4NZb76VFi1RCQ5vSsWMvvvpq1gmvq0uXPoSENCEhoSNTprxYZa5Hbm4eY8feQmxsIhZLM84550I2bdpy7Pnp078gIqIl8+YtJC3tDMzmxmzZsvWEMUSYCaRE2rT5Ddc1igaXiutoUHigNfylIAVwxkSw5d17ybzjYuJ+WkXa5U8Run2fX2zxJIfGdmXz/NEYjpTQud80In7P8LdJXsEwKobQhSnIPBcl/dNxLv3Pae48is4MZ3yaT/sHi9n5QShLLozCUdiwcsODDlsDwRLlDvA47bBkyR+sX7+JefNm8vPP359y7MGD2Vx11XWMGXMlmzat4vff5zJ69OWVjj169CjmzVtIXt6/a66LFy/nwIFsrrjiEgAef/xpPvroM9544wU2blzJQw/dwy233MvcuQtOGOuxxyZx883XsXHjSi64YDiPP/4MGzdu5ocfvmTz5j/54IM3ad682Qnn6IwCRS+w5TkZPvwyliz5gw8/fJONG1fy4otPH2tt9ddf/3D55WO56KLzWbduOVOmPMGzz77KW2+9X+lrGzfuVv788y++++5zVq78hZCQEIYNu5TS0n+jDVarlSlTXuTtt19h48aVJCS0OmEMdwFdoV2HrXEMAK7DlUcbgsID/+LPJdJ9N49k0wcPoi8oofMVk2j03VL/2OJBCvrHs37ZOBxNwugwbAaNP1zrb5O8gv4Mt4JUxOkpGbod++f/Od2dRxEKdHm6iNPeKSD7VyO/DoqmZF/DcYP0/jYgSM0whbqbwTvtYDab+PDDNzGZKk6g3L//IA6Hg0suGUlCQjwAnTp1qHTsc889k4iIcL799geuu+4aAL74YiZDhgykadMmFBcX88orU5k//1v69+8DQOvWCaxe/TdTp37A8OHnHhvr9ttv5NJLLzj2eM+evXTtmsbpp7s7kCUmxldggcAYqWfh/EWsWLGaDRtW0L59OwCSkhKPHfXKK28xcGBfnnzyEQBSUtqyY8cunn/+NW6//cZTRt2+fSc//vgTv/02hwED+gLwySfvkJjYmc8/n8n117ujii6Xi9dee54ePbpW/Abp3HlsMlubDpu+3GE7eAQ6VCS6DqIFrB9di3n8x36Zu6CXW0Wa8uC7JE/4kIi/t7H7sWtQzQ2396KtTTQbll5LyujvaHvLPELTc8h49kzQNZwf4JqgJJmwLE2lZNROrOMykLtsGCc0Q4iGFR3SEm3GlxLaysXyKyL5uV8MA77PI7qrNq/vxxNYn+wAxxIlcTqgY8f2lTprAF26dOLMMweRltaXSy8dw9tvf8jhwzmVHq/X6xk16iJmzJgJgM1mY9asHxg9+jIANm/eitVqZdiwy4iIaHlse+edj9i1K+OEsXr06HbC45tvHs/Mmd/TrVs/HnjgcRYvXl6hDcYIPeu3bKJZ0ybHnLWTSU/fRp8+vU7Y17dvb7Ky9lNQcOpy4JYtW1EUhTPOOP3YvsjISDp37nDCsqder6dr186VvDtulDAT0u5EtVafl+drdE3jAHAeCt59ax1/5rU5GkWx6f372Xvj+TSZtZTOV07GnHHQb/Z4AlekmS3fX87+20+j+Wt/0v7ir9EV+D3d2eOIaD2hc5MxXBOLbfIBrOODCtL60uxsO2f9novQwa+Do9n/k/ZvXoIOWwPCEglIMJtCqzxOp9OxYMEs5s//lrS0jkyb9hnt2vVg3boNlZ4zevQoFi9eTlbWfubOXYjd7uCii0YA7nw2gNmzZ/D330uObRs2rGD+/G9PtNFyom3nnXc2u3ev5957bycn5wjnn38548ffdsr8xgi9O0+simuQlLLSu8qK9lelBDr+eJPJhE5XdWFFEe7OY7P/mVnlcf5AFxsJeh2ug5U75UG0gz+dNvQ69t51ibsXafZR0kY9SeyCBt5oXa+Q8fI57HxzKFELd9F5wMeYMvL8bZXHEUYF8wcJmJ5sjuPzo5QM2448qv2okJaJ6uxuHB+e7GLpRVFsfzfE3yZVSdBhqwVNmlTsTVS239OEhAMCXDX4jgohOOOM05k48SFWrVpE8+bN+Prr7yo9vlevnrRp05ovv/yWL76YyQUXDCMszN2nskOHdphMJvbs2UvbtkknbOVLrlURFxfLNddcwbRpU3n//df55JMZ2Gwn3gULnaBr1zQOHso+Jem/nPbt27F8+coT9i1fvpKWLZtXqJDt0KEdqqqyYsWfx/YVFBSwYcPmSqN4lVHeCN66eGetzvMFQqdD1zgG54GqHbZgHpt28KvThrsX6bpvJlHapjnt7n2LxGe/QDga9o9/9o092Dz3Soz7C0nrO43wPwKgTddJCCEwPdqMkE9a41pVTHG/dNQdQQVpfQhprjJkUS7Nhtr5644I1j4UVmXgwJ8Ec9hqwf79/lXhCQEGI7iq6XqwcuVqfv11MeecM4QmTRqxdu0G9u7NqtZJueqqy/jww0/JyMjk228/PbY/PDyc++67nQcffBwpJQMG9KGoqJiVK1ejKAo33ji20jGfeGIK3bp1oWPHVJxOJ999N4ekpMQKl3TPGTqI7p26ctmlY3jp5SnHctSKi0u48MLh3Hvv7fTqNYSnnnqWK6+8lNWr/+bll9/imWcer3Du5OQ2jBw5jFtuuZd33nmFqKhIJkx4moiIcK666tIq34tT0CkIox7rkl21O89H6Js3xnngsL/NCFILyp02f+W12ZvHsvHjR0l46Suaf7qQsA272PbSrdibxvjFHk+QP6Q165eOpf1FX9PxnM/Z+c5wDl9ddbpDQ8RwRQyilZHSS3dQ3D+dkG/bou8T5m+zGiyGMEm/b/NYe184W1+xULxbR+/p+eirXszyOcEIWwNDb3Av9VmLKz8mMjKC5ctXMnLkFbRr15MHHpjAhAn3c/XVlStFwb0sunXrdiIjIzj77MEnPDdp0mM88cTDvPzym3TufAbnnnsRs2b9SOvWCVWOaTIZefzxp+nWrT/9+w+lsLCQ2bNnVHisOdrIF699TK8epzFmzE107NiLe+555Fitue7du/DVV9OZNesH0tL68OijT/HQQ3dx2203VDr/Rx+9xWmndefCC6+id++zKC0tZd68bwgJqX3oW5j02Fbt0WQem755I5xZFZdtCaJt/Bltk0Y9GY+MZutLt2LZto8ulz5B5IpNfrPHE1jbxbJh2VgK+7QkefwPxE/4DVSNFlGsB/q+YViWpiKi9ZScsw3Hl4FXk86XKDro/koh3V4sZN9sE7+dE431kLaEHSKQ+pX16NFWrlz5UoXPbd/ektTUhq+gU12we70gqrEktoW/rfE0kqMbi9GHKES00ditDbBlbTrGnmNo+svNmAdo67OU+8YX5L/3DQl/fYUwVt0z76OPLqjy+SD+wV+RtnJCdu2n3d1vErLrAHtvv4h9N44ApeHe0wuHi9Z3zqfph/9w5MJ2bJ82EtWi/cTy2iKPOim5bCeupUWYnmyO8ZGmQQVpPdk328SKMZGYm7oY8H0eke29V5R8rHHsX1LKnjU5tuF+G/+jKDoICdhm8AJjpA57oVOTrXSESQ+KoPR37eWx6Vs0BlXFWQPhQTCXTZv4O6+tNKk562dMJGdYL+LfmEX7215Fn1fkV5vqgzTo2DV1GLtfOIuYH7bRafAnGLMCr7i0iNETOi8Zw1Ux2J7cj/X6PUi7RpOwGggtL7Ax5NejuEoEvwyMIXuxNhrHBx22BoglSmK3Vt0MvqFijNQjVXAUarDNkiIwdm2BdYkGHbaWTQBw7sv2syVB6oO/nTbVYmb7czexa8I1RP6xibRRT2LZlOFXm+qFEBy4qxfpsy4jZEcunftOw/L3AX9b5XGEScE8LRHjhGY4Pj1CyYgdyNyGLSLxN7E9nZy19CghTVUWD4tm92dmf5sUdNgaIpZI97/FeX41wysYw/UIAbYCbV5szAOTsK3cg1qqrTw2Q6umQNBhCwT87bQhBAevPJONnz6KcKl0vvppGn+z2L821ZPcYclsWHwt0qCj0+BPiJmV7m+TPI4QAvPE5pg/SsS1vIjiAVtRdwXgXb0PCUtUOWvJUeL6Olg1PpKNky1+XfwJOmwNEL3R3fmgombwDR4hMEbosec70WK3dfPAtmB3YVuR4W9TTkDXJBYMehyZgRc9+C/izx6k5RSltWHdN09R0LMdbZ+YRpvHP0Sx2v1qU30o6dyYDcvGUtylCalXfEuL/y3TZOpFfTFeHUvo/GTUQw6K+6fjXNlwl7W1gDFKMnBOLq3HlLJxchirrovA5aevQdBha6BYIiXW4prVZGtoGCP1uGwqLqv28jDM/VqDTsGqsTw2oSgYWjXFubdmleuDeWwNA387bc7ocDa/cx97b3J3R+h09TOY9jXc8jGOJmFsWng1h6/sRMITi2k77geENfAuovr+4ViWpkKEjpKzt+GYGVSQ1gedEU5/v4BOTxSR8VkIi4dHY8/1fcAk6LA1UMKi3PGn4vzqjmx4GCPc5QHtGlwWVSLMGHu0xLp4h79NOQV9q6bBCFsA4m+nDZ3C3jsvYctbd2POOkzaZU8StXS9f22qB9KsZ/v0kWQ+OZDGX2yk47mfYzhURZ2kBoouxYxlaSq6HqGUjt6N7fmDBFJVCF8jBHR6rJje0/PJ+cPALwNiKNrtWxcq6LA1UIwh7iK6gZjHphgV9CFK2bKo9ggZ1Bbb6r2oRdrKDzEkNMeZeSB4UQ5A/O60AbmDurLuqyexN4uh/S2v0HLq96BqLwpeI4Rg36P92PrFxVjWHqRzv2mEbGq4kcPKUOL0hM5PQX95NLYJWVhv3oN0BK8P9SHxKiuDfsrFekjh536xHPnTd/0Hgg5bA8YSJSktEJpto1EfjBF6HEUupEt7Fxfz4DbgVLEu2+1vU05An9gcabXjyg42gQ9EtOC02eIbs+HzCRw+vw/xb33f4Et/HLm0PZsWXYNiddJ5wHSi5msvcl5fhFkh5JPWGB9pimPaEUpGbkfma1CF34BoPMDBWYuPog9XWXRWDHu/O7VzjzcIOmwNGEuku4B3SeCVFsIYpUdKbS6Lms5IBKMO6+/aurgbEpoD4MjIqtHxwTy2hocWxAhqiIkdU65n5+Nj3KU/Ln+K0C17/GpTfSjq2Zz1y8djax1F+wu/pulbqwNOjCCEwPxUC8wfJOBaXEjxwHTUDG2tEDQ0IlJdnL30KFFdHCy/IpL0V0O9/rEJOmwNmJAw0OnceWxDhozgjjse8LdJHsNg0aHohCYdNiXUiKlXAtbfNOawtXa3vnDsrpnDFqTh4m+nDSHIvmIIGz95BOFw0nn008T9+Id/baoH9lYRbPj9WnKHtSXpnoW0vmsBOANv6cI4Jo7QucmoWW4FqWt14OXu+RJzI8nghbm0usjGPw+G89ed4ahe/MkKOmwaZ9y4Wzn//Ep6gAoIjZQU5wu++eZTpkyZ6FvjjkOni+abbzwZsdF2eY+QQW2w/7MfV26Jv005hq5xDCLUHHTYTkJKF9K2HbVwPq7cj3DlvITr8DO4Dj+NK+cFXEffQc3/BrXkD6Rjf4PJAfS70wYUdWnL+q+fpCgtiZSH36P1M58i7Nq7yaoJapiR9JmXknVvb5q98xftL/gKXb7V32Z5HP3gCCxL2kGoQvFZW3F8l+tvkxo0+hDo80U+qfcWs+PdUJZeEoWj0DsKUt9lywUI2dkzyciYhM2WhcnUgsTEiTRpcpnf7DGG2ik8aiLUGI05zG9meAVjpB5rrgNniQt9qLY+qubBbWHyz1gX78RyYWd/mwO4lz0MrVvg2L3P36b4FSkl0rYeWfA9avEiZOlqkKU1H0CxIIztEeauiJCeiNAzEKaOCKHzntF1xPrRtX7vQeqIi2TTBw+S+PLXNP94AZYtmWx9+VYcjaP9aled0CnsefZMStvFknTbT3Tu/zFbvh+FLakBvpYq0LUPwbI0ldJLdlJ6xS7UZ1tivLtxsAdpHREKdH22iLAkF3/dGc6vQ6IZ8H0eoS08G6X1WYRNCGESQnwohNgjhCgUQqwVQpxXybFjhRAuIUTRcdsgX9laGdnZM9m+/S5stn2AxGbbx/btd5GdPdNnNpRH3J5//lXi4zvSPq0jQsDZ5564JDpr1o907doXi6UZcXGtGTx4ONnZhyod9913p5Ga2pPQ0KY0adKWoUMvwen890552rTP6dSpN6GhTUlN7cmrr05FLVOIJSWlAXD55WPR6aKPPS4fNyWlO2ZzY1JSuvP++x/XeN5129dx+e1X0yw+haioeAYMGMqKFX/W/030AKbT4xGhBu0tiya1xLGr5g5bIOWxSdWK6+j7OHd2xbmzK67DT4FaghJ9I7rm09AnLsWQvAtDah6G9jYMHewYUgsxpGShb/MP+vh56Jq9hRJ1HegiUQtn4TpwM86dXXCkx+HIvBDXkbeQ9l3+fqknoIVIG3odGQ9eydYXb8GSvoculz1J+F/b/G1VnTk0riub512JIbuItL7TCF++198m1Zm8ojymfDqFvKK8E/YrjQ2ELkxBf1EUtof2Yb0jE+msXXS5srFr+nyg0fbGUvp/n0fRTh0/948hb71nAw2+XBLVA3uBgUAk8DjwtRAisZLjV0gpw47bfveNmZWTkTEJVT3xTl1VS8nImORTO5Ys+YP16zcxb95Mfv75e0LD5QkFdA8ezOaqq65jzJgr2bRpFb//PpfRoytZVgXWrFnLHXc8wOOPP8iWLX+ycOF3DB165rHn33//YyZMmMyTTz7Cpk2reOGFyTz//Gu8/fYHAKxatQiAd999jays9GOPv/tuDnfe+SB33XUz69f/wZ133sztt9/Pjz/+VKN5i4pLuPyiS5jz8SxWrvyFLl06M2LEKHJy/K+CFEY9pn6tteewtW6J6+AR1OJaRJQaOFJKXHlf4NjRDteBG0Eo6Jq9haHdQQxtVqNv9iq66LEoln4IY2uELhKhGBHCgNCFIQzNUcxdUMLPQxdzK/pmr2FI/AVDuxwMyTvQtfgEJeJSpHU9roO349jeBseOTjizH0MtXauJJVRNOG3AkfN6sWHGRFyhZjqOf46mn//SYBP4CwYlsmHZOJwxIXQ893MafbbB3ybVidnLZrN933Z+WPbDKc+JEIWQL5Iw3t8Ex3s5lFy0A1lQcwVpVWPX5PlApPlQO2f+lgsSfhkczYGFRo+N7TOHTUpZLKV8UkqZIaVUpZRzgN1AD1/ZUF9stopzgyrb7y3MZhMffvgmnTp1oHPnjliiQKrgKvue7d9/EIfDwSWXjCQxMZ5OnTpw/fVjaNKkcYXjZWbuw2IJZeTI80hIiKdLl87cffet6PXuu4NnnnmBZ599kksvvYDWrRM4//zzeOihu3n77Y8AaNQoDoCoqEiaNm1y7PHLL7/B1Vdfzm233UhKSltuv/1GrrrqMl544bUazTtkyADGjLmCpGZJpLRpy+uvP4/ZbGb+/F+89dbWipDByTjSD+E8oB2ZrqFNKwAcOxtuRKA2SMdBnJkjcGWNRuhi0ScsRJ/0N7qYWxH6ij/vNUUIgTC2QRd1DfoW72NM2YWh7TZ0TV8BfWPUnOdw7uqOY0c7nIeeQNr867xrQUEKUJLckvVfTSSvbyeSpnxG20c/aLAtrazJMWxYOpbCPi1JHv8D8Y//5pbmNxDyivJYtn4ZUkqWrl9aYaRLKALzlJaY30nA9UsBxYO3ou6t/v+rurFrMnegEt3FydnLjhLW2sWSC6LY8UGIR8b1m+hACNEESAE2VXJINyFEjhBimxDicSFEhbFFIcSNQog1Qog1OTne/eE0mVrUar+36NSpPSbTv3VfypvBO8tU2l26dOLMMweRltaXSy8dw9tvf8jhwzmVjnf22YNISGhFmzZdufrqG/j44xkUFhYCcPhwDnv3ZnHLLfcSEdHy2PbII0+xc2fVdci2bNlGnz69TtjXt29vNm/eWu28AIcOHebuxx6kzyWDiG2USGRkKw4dOszevdrI0TIPaQugqSibscxhs9fCYWuoy6Jq6Wocu7ojixeha/oa+qQ1KGFnezUPR5iS0cXejSFxEYZ2B9E1ew9haIV6eDKOHck4dvfDlTsNqfpPfacFp80VYSH9zbvIvO1CGv+w3N3SKqthFqZ1xoSwee6VHLyuKy2f+4OUq2ahlDj8bVaNmL1sNmpZoU5VqlVGuozj4wj9MRl1j43ifum41lYtqKpu7NrMHYiEtlA587dcmp5tZ82tEfzzSFi9a6b6xWETQhiAz4GPpZTpFRyyBOgENAYuAa4EKqxZIaV8T0rZU0rZMy4uwlsmA5CYOBFFOdFTVpQQEhN9q84MDQ094bHOAIoOHDb3D5VOp2PBglnMn/8taWkdmTbtM9q168G6dRWH9MPDw1mzZjFffjmN+PiWPPfcK3To0Iv9+w8cy1ObOvVl/v57ybFt/fo/2LBhRbW2VvTjWb6vqnkBxo69hb/++YfJDzzB/C9n8/ffS2jZsjl2uzYulsYuzVFiQjXlsOlbNQWjodYRtobmtKlFi3DuHgTChD5pFbrYOxHCt5czoY9DF3MDhsRfMaTsRdf4WaTzMK7943FsbY7zwB1I2xaf2lSOFpw2FIV9t17obmm17xBpo54ickVl9+faRhp07Jo6jIznziT2u3Q6nfkphgOF1Z/oR8ojXK6ypReXy1VtpEt/VgSW31PBICgevBXHnIqPrW7suswdiBjCJf1n5dH2xhLSX7Lwx+hInPXIVvG5wybcV9VPATtwe0XHSCl3SSl3ly2dbgAmAZf60MwKadLkMpKTX8NkagkITKaWJCe/5leVaDmK3t0I3lnmywghOOOM05k48SFWrVpE8+bN+Prr7yo9X6/XM2TIAKZMeYJ//llGcXExc+YsoEmTxrRo0Zxdu3bTtm3SKVs5BoPh2JeznPbtU1i+fOUJ+5YvX0mHDu2qndd97Cpuu+1GRpx/Dm2atiE8zMKBA9n1fas8hlAUzAOSKF20XRN5TABCr3MrRbdn+tsUr6GWrMSZOQJhTMLQegWKOa36k7yMMLRA1+ghDG3T0ScuQQkfiZr7Ho4dHXBknIVaOAfp45YkmnDacLe0Wv/VEzjiIulw44s0/2hew8xrE4L99/Qm/ZvLCEnPIa3vNELXaed6dDLHR7jKqUmkS9fJrSBVUs2UXroT25unitWqG7uucwciih56vFFI1+cK2TvLxG/nRmM9XLdVAJ/WShDu0MqHQBNgmJSypqESCWhCb9ykyWWacNBORlf2P1mSB5t3rubXXxdzzjlDaNKkEWvXbmDv3izat29X4blz5sxn164M+vfvQ0xMFL/9tozCwiLat08BYOLEh7jrroeIiorkvPPOxuFw8Pff69m/fz8PP3wvAImJ8SxatISBA/tiMpmIjo7ivvvu5PLLx9KjRxfOPnsICxb8yhdfzOSbbz6p0bwpKW344ouv6d6xC9lbc/nfXc9hNHougdMTmM9MpuT7jTh35GBIbuRvcwAwto3H+lfDjGRUh7TvwZk5Agwt0Cf+Wu88NU8jhEBY+qNY+iOdL6Pmvo/r6FScmeeDMQVd7H0oUdcgFM/ktFSHFsp+AFgTmrL+i8dpO+EDEl/6mrDNGeyYdB1qqG9a+niS3PNT2PDbGNpf/DWdB33Mtk8vJHdEir/NOoWdWTtPuYl2uVzsyKp+RUBpZsDyawql12Zgu3cvcqcV04utEDpRo7HrM3cgIgSk3lOCJcHFyrGR/DIghgHf5xHRrnYtwnxd3OptoD1wlpSVF0YqK/fxt5QyWwiRiltR6rvaGQ0QRXEvixblCyIjI1i+fCVvvvkeeXn5tGrVggkT7ufqqytWikZFRTJ79lwmT36ekpJS2rRJ5L33Xqd//z4AXH/9GCyWUF566Q0efXQSISFmOnZM5dZbbzg2xgsvTOb++yeQkPA5LVo0Y9eu9Vx44XBee+05Xn75Te6551ESElrx5psvcv7559Vo3g8+eIObb76HPoPPpklsYx69736O5PpfIXo8IUOSAShdtF0zDpshOZ7iuUtQC4tRwi3+NsdjSOnAue9ykA4M8XM156ydjNA3QtfoUZS4B1ALvkHNeQnXgZtwHZ6ILuYulJhbEbpIr9uhFadNtZjZ9vJtFH84j/jXviFk537SX7sTW7y2/x/zivKY+t1Ubr3oVqLCogAo6dqU9cvG0f6SmaReMpOM587iwF2nu3+Zfcye7D08+9mzPHL1I8Q3iT+2f9J19ateICw6Qr5KwvbwPuyvHULNsBPyaWtEmK7ases7d6DS6mIbIS1yWXpxFL8MjKHfN3m1Ol/4ailHCJEAZAA24PhS2DcBS4HNQAcpZaYQ4kXgGiAMyAY+AyZXF5Hr0aOtXLnypQqf2769Jampber7MjTNkSzIOyRonSZRtFfjs14U7CzBWaoS08mCv4Kt6ek7SU4+UfAgpWRf2ymYerai8Vdj/GLXyZT8vppDtz1D00//h7l7+1qd+9FHF3jJqvrjOjQZ1+GJ6Ft+jRKpvSh3dUgpkSW/4zr8LLJ4ISiRKLF3oou5G6GP8YkNWnDcACKXbyTl/rcRSLa9cAt5/bRRfLoiPp7/Mb+v/Z3B3QYzZuiJ33GlxEHyuB+I/S6dg9d1ZffrQ5EG3158H33vUfbn7KdFXAueufEZr8xhf+cQ1rv3oqSFEPp9W5Tm2lrpaGgU7dKxeGQUxRk65tmH/SWl7FmT83xZ1mOPlFJIKc0n1Vf7XEqZWfZ3Ztmx90spm0gpLVLKJCnlxFosn/5nsUS5U0MCshl8pB6XXcVl1VZ/PyEEIYPbYl28E+nShm3GlAQA7NsbbkPuk5G2HbhynkGJuKJBOmvg/qwolsEYEhegT1qDsJzpVpduT8SZPQHpPOp1G7SS15bftxPrv34CW9NY2t/8Mi3en6PJvLbqSlOooQa2zriYfQ/2oemH/9D+/C/R5fquBuKe7D3sz9kPQFZOFpnZ3sldNd7cmJDv2qLuKFOQrtdOS76GSFiSi7OWHCW2d+3cmmAv0QDCbHHnshXn+dsSz2OMdK/eu3uLagvzkGTUoyXY/9FGD09ds0aI8FAcWzP8bYrHcGY/BMKArunL/jbFIyghPTDEf4u+zXqUsKGoOc/g2N4a16FJSJd377i04rTZWjVmw+cTODL0NBJe/YaU+6aiFGurd2eNSlMogsynB7P9g/OJWJpJ5/4fY9rpm/6c785+t8rHnsRwXiSWRe1AQvGgrTgX5Httrv8CphjJoLm1+5wEHbYAwxIlKS4QWrxZrReKQUEfqsOmSYfNXY+t9NftfrbEjRACY0oi9gBx2NTSv5GFs9DF3o8wNPO3OR5FMXdG3+pr9G3WIyxn4jr8BI7tSbhyXkaq3nNetOK0qaEmtr1wCxn3jSL25zV0Hv00pszKW+j5ktqWpjg8Jo3N80djyCkhrd80wpd5V6l9fHStHG9G2QB0XUOxLEtFaWOi5MId2N9rmLX1tIKulpqboMMWYIRFguqCUm2XCKoTpkgdziKXZpYey9E3jcDQsamm6rEZUxKxb8tAqrV7r7RYj82V87+yfK+7/W2K11DMnTHEz0KftBph7oEr+z4cO1Jw5U5HytopyWqKVpw2hGD/+GFsfu9+jIdy6XL5k0Qt838bqLqUpijoH8+GZWP/bWf16Xqv2VdZNM2bUTYApYURy6J26M+JwHp7JtaH9iEbUPeHhsx/ymHTSq0sbxIS4VaMFgdgtNoYqUfin2XR6j47IWcmY122G7VUG6mWxnaJyBIrzn3arRNVE6RjL7JgFkrMzT5RVPobJaSnO8ct4VeEvimu/eNw7uyGWrTAK/NpxmkD8s/oyPqvyvLabnmZFh/M9WteW01LU5zc4NzaNob1y8ZS0C+e5Ot+JHTiPK80SD+cV3F061DeiRHK+jZgr+h8Ea4j5Nu2GG5phP2VbEqv2IUsOfXm8L/W/P1kPP36a+SwCSHMQoiHhBALhRD/CCHWH795xBIvYzC4sDbQfna1QQgIjZAU52mibJ1H0YfqUAwCe753Ig5VYbXaMRgqn9c8JBlsTmx/VN2uy1cYU1sDYE/Xhj11Rc39CJDoom/2tyk+RQkbgr71KvQtv0aqxTj3DMWRcQ6q1fORJ630IIXj8trOOY2EV2aS8sDbKCU2v9gy6bpJTH90OoO7D0YIwZDuQ5j+6PRTSlZU1ODcFR3CljlXkD2+K99tmM/2zG38+Pv3Fc5T1wbp7z/4PtMfnX7K9v6D73tk/OrOF3qB+dVWmF5siXN2HsVnb0XNdtTo3P8Knn79NY2wTQUexl2W43vg25M2zRMbe5SsrP2UltoCPtJmiXJ3PLAFnJBHYIzQYy9w4q6l7H2klJSW2sjK2k9sbOUqPvOAJDDoKP1VG8uihuR4UJQ65bFpZVlUSokr7xOEZQjCmOhvc3yOEAIl8jIMbbega/oK0roG586uOPffjHR6PndIK06bGmpi24u3sOeey4idv5rOVz+NaZ9/cqXq0+BcGnT89UIfvj2tGClg2dolFO/aX6vxvW1/fc8XQmC6swkhM9ugbrK6FaSbSz0yd0PHG6+/poVzLwQuk1L+Uu8Z/UR4uA3IZv9+Bw5HgBUpOwlVhSM5gvz1bhFCIOEscVGa4+DgOiM6k29W9A0GF3FxR8s+QxWjhJkw9YrH+us2YJhP7KoKxWzC0LoF9i276nT++PGz/V6TTVr/AsculEaP+dUOfyMUI7rYu1Eix+A6/BTq0amo+V+iazQRJeZ2hOK5mlhaKbKLEGRdP5zidq1IefAd0kY9ybaXbyO/dwefmlGRSvT4WmzVPr/8B1w6wOV+fsnEl7nkwQcoSWtSo/O9bb+nzjeMjEL5NYWSi3ZQPHAroV8lMdvu3demdbzxf1tTh60EqF03aQ0SHm4jPPyAv83wCY/dbqAgB95Yq42cKk9hL3Qyve8SOt/WijOeS/a3OScQcmYyeZN+xpVTjC7O/x0GjO2TsK7e6G8z6oxaMBvQoYRrt5ivLxH6GPTNXkPG3ILz4D24su/Dlfse+mavo4Sd47F5NOO0AXn901j/5ROk3vEaHW58kYz7L+fANef4pKNAZSrRkf1GEhUWVevnHXr4PuUItw37kNz3LmP3gEZVnu9t+z19vq6HBcuy9pRcsJ0DV/zDsruX4sI7r03r1Pe9r4yahiieB+4ta9wepAFw+vkqezYpHNjpb0s8izFcT/OB0eyZm+NvU07BfFYKSKkZtaixfWtc2UdwHcnztyl1Qhb9hAjtjdDH+tsUTSFMqRgSfkIfPwdw4dxzLo7Mi5D2DI/NoZXlUQBrQhPWz3ico4O60vq5GbR99AOEzfv5yPVtcF7R8y6jwhtDC0m9eCY/v/2BVxuk17cBe13OV+KNWH5PZeGof1Cd/93m7/V97yujUgdMCPFD+QacBVwO7BZC/HT8c2XPB9EYvc53e/Yrfwi85d+EYXHkbSshf4e2kvRMPVoiIs2U/rrN36YAYGzvbsVm39LwhAfSeRRp/RvF4rnIUaChhA/H0GYjusZTkEULcexoj+vw00jVM0n6WnLaVEsIW1+9nczbLqTxD8vpNOZ/GA96tzNEfRucV/S8U3Wxqpeeo8OT2ZW53SMN0itTItZV5Vrb809GROrY0yUHl/4kZ7UBNn+vq8qzru9ddVTaS1QIMa2mg0gpx9XLCg9RVS/R/yJ39jAQGgnPLgqsZdGCXaV8kfoHfV5MJu3O+OpP8CGHLp2Obd1+Wm57BOGHRtDH4yooYu8ZVxN199VE3XBpncbwVx6bWjAb594L0ScuQbH094sNDQnp2Ivz4L3Igm/AmIy+2VsoYWd7bHytLJECRC/6m5SH3sMVYmTra3dQ2E1bqRE1wqWS8NhvtHh5JbnnJLHt84twRZrrNFRVvU59cX5lSCmxv5iN7bEsdH0shHzTFiWupllY2sBb783xjDWOrX8vUSnluJpunjM9iCfpPVIl/Q9BfoAVo45ICiG6vYU98zS4LHp2Cq49uTh3+N82XUQY+lZNsG+um/DAn6ilK0AYECGn+duUBoEwtMLQaib6hPmAxLnnHJx7r0Q6PJOzq6VoW+6Q7qyf8TguSwgdxz5L45m/+9uk2qNT2PPsmex4exiRizLoPPATTBl5tR7G2yrQ+iCEwPRAU0K+SML1dwnF/dNxbdNW67Gq0KLKtaZ12BYJIaIq2B8hhFjkcauCeIReI1VUVbB6XuClHiYMi+PAkjzNtaoKOTMFgNJftLMsat/c8BIZZekahKkzQqlb1OG/ihJ2LoY2G9A1ehK18DscO1JxHZ2KPCmfpi5oyWkrbduC9V9OJP/09rR9cjqtJ3+CcGjrWlATDl3XjS1zrsC4v5DO/aYTtqp2/Yhr1OvUi+fXBMOl0YQuTIF8FyUD0nEuaxhteHzx3tSWmv6SDwIq0o6bgeB6hUZJ6iqJayVZ9UMAOmwj4lCdkn0/H/G3KSegbxOLPjGa0l+00VfU1LEtzn3ZuPIaxkUS3Esp0voPwtzd36Y0SIRiRtf4CQxtNiBCTsN14Dacu/t6pOiulpw2V6SFLe/cS9a482j25SI6XP8C+qMF/jar1uQPac2GJdeihhnodNanxH69uUbn1bbXqafPrw363mFYlqYi4vSUDN2O4wttXbdPxpfvTW2o8pdcCNFdCFF+1Uwrf1y2nQbcCNTuliCIzxACep2vsvYXJeCK6DbpFYEpRq+5ZVEhBOYzU7Au3ol0+r4jw8kYO5UJD+oYZfNLEV1nNriOIMydfT93ACFMyegTfkbX4hOkfQfOnd1xZj+GVEvrNa6WnDZ0Cnvuv5xtz91I2IZddBn1FKFb9vjbqlpTmhrH+mXjKOrZnHZXf0fLKcuqbcvlDxVofVDamLAsTUV3hoXSsRnYnt6v2SL2vn5vakp1oZc1wGrcZeUXlj0u31YBjwCTKj07iN/pPdKFvVSw9ufAirIpeoX4c+PI/OkIqktbX/qQs1KQBVZsf2b625RjSlHbRm1E/GqCtG8BQJja+9mSho8QAl3UNRjapqNEjUbNmYJjZxfU4sX1GldTThuQM6IPGz99DKSk89XPEDv/T3+bVGPKlYg5Zjub5l/Foas6Ef/kYtpe9yPC5vS7CtST/TBFtJ7QuckYro7BNukA1uv3IO31X66vK55WyHqb6iQbrQEB7AJOB45PX7cDh6SU/g8jBKmUjv0llijJqh8Vel/gvy+GN0gYHsf2GQfJXpVPsz5R/jbnGObBbUERlP6yHXOf1n61RRcZhr5VU+ybGk4em7S5nUthTPGzJYGD0MeibzEdNfJqnPtvwpkxCCX6JnRNnkPoIus0ZrnTphUFaXHHRNZ/9QTt7n6TdvdNZe/Wvey94yJQtH2zeny/yTFDx7Bj2kisyTHEP7UEU0YeD9/hOOH5csp7mlanZDx5/JPPr6199UUYFcwfJqIkmbBNOoCaaSP06zaIaN8rSOv73viaKj/JUso9UsoMKaUipVxT9rh8OxB01rSP3gA9h6r8OVfB1fBycquk1TkxKHpBpsaK6OpiQjH2aIlVK8KDTm2xbWw49Y+kYzegB0NLf5sScChhZ2FouwEl9j7U3Pdx7OiIWji3XmNqKdrmiItk00cPkn3JAFq99yOpd7yOrqh+S8DepEIlohDse6w/Wz+9kNLNmSzbULdepjV5vk72eQAhBKYJzTFPS8T1RzHFA7ai7vJM/cCaokUVaHVUVTh3TE03XxocpPb0GqlSeESwZYV/64J5GlOUgab9osjQmMMG7mVR2+q9uPL8/2Nh6tQW18EcXDl5dTrf53lsjj1gaIUQgVf0WQsIJRR90xfRt16B0EXjzByBc9/VSGfdE8G15LRJo4GdT41j12NXE710PZ2vnIx5T7a/zaqQqpSIRy7vyNPPxqDiTvmQrlNzqKpTMmpdRWocHUvoT8mohxwU90/HuarIo+NXhRZVoNVRVYTtrZO294HpwEdl2/SyfW961cIg9ab7uSp6Y4CqRYfFkbu5mILd/neMjifk7BRwqZpoU2Xq7C4s2lDy2KQjCxGMrnkdJfR09El/oTSaiJr/FY4dHVALZtV5PC05bQjBwavOYtP7D2A4WkDnKyYR+Ye2+upWp0TMK8rjt0NrcZStFDqli2V/Lznh+erObwgqUv2AcCxLUiFCR8nZ23B8m+vR8StCqyrQ6qiqcG54+QZcAazHXcLDzL/lPP4BrvKBnUHqQWg4dBmisupHXXXCowZH4og4AM2pRU29EhDhJk3UYzO2bwOKgm1DA3HYnAcR+qb+NuM/gVCM6Bs/hb7NGoShBc69l+DcewXSWbfvk6acNqCgV3vWf/UE9qbRdLjpJZp9sqBa9aWvqEsvUul08ttLb4Mq693rtL72eRJdO7NbQdo1lNIrd2F78aBXFaRaVYFWR01DLi8Cd0opl0spnWXbcuBuoEa9oIQQJiHEh0KIPUKIQiHEWiHEeVUcf48Q4qAQIl8I8ZEQwlRDW4NUQK+RKgd3CfZsDKxl0ci2oUSlhGquGbww6DAPbIN9zV5/m4ISasbQtlW9HDafLou6DoOuke/mC4Ji7oI+aRW6xpNRC2e5c9sKvqvTWFpz2mwtG7HhswkcHdLd3Tx+woc+aR5fHXXpRerQw7acDNpdOYude3fUq9dpfe3zNEqcntCFKegvjcb2aBbW2zKRTu84bVpVgVZHpb1ETzhIiFKgl5Ry/Un7uwArpZQhNRjDAjyAeyk1ExgGzAA6SykzTjr2XOATYAiwH/iubJ6Hq5oj2Eu0co4egLEJJq56wskVjwWWVmTFQ9vZ8NZexh4YgDFcO73qXDnFKNEhCJ3/l6JzJr5JyS+raLX8k3r1OPV2b1EpXTg261EaTUTf+CmvzhWkYlTrelxZY5HWtSiRo9E1fR2hj6nTWFpQkOYV5TH1u6ncesEtdP7kd1q9PZvCLm1If+0OHI2i/n3+oluJCouq/Pw6Pu9RpKTZ63+S+OAvFPVoRvq3l+FoFu7dOX2MVCW2ifuxP38Q3TkRhH6RhIioOJ/V2++9L/5vPdJL9CRWAa8LIVqU7yj7+xVgZU0GkFIWSymfLFOdqlLKOcBuoEcFh18LfCil3CSlzAUmA2NraGuQCohpBu16qYGZxzY8DtUu2ffzUX+bcgK6OIsmnDUAU+cU1PxCnJkH/W1K1ajuSvVCifKvHf9hFHOaO9rW6El3btvOTqiFP9VpLC1E246VbvjjR/befhHpr9xG6La9pF3+FJaNu08o7VDl+XV83qMIwYG7epH+zWWEbs4hrd90QtdrU1BRV4QiMD/dAvO7CbgWFVA8aCtqZsURUW+/9z79v60BNf01uQ6IBTKEEBlCiAwgA2gM3FCXiYUQTYAUYFMFT3cE1h33eB3QRAgRW5e5grjpPVJl51qFw/5fpfMoTftEYorWkzEnwLrce5BjwoMN/s+pqxJXWQstXYR/7fiPI4QBXeMn0Cf9idDF4swchnP/jUhX7Vuc+dNpq6h0w9FzTmPDZxNAUWh84zMsX7vEb2Uz6kru+Sls/G0MuFQ6D/qEqJ+0vZRXF4zj4gj9IRk10+ZuHL/2xHY93n7vtVj2o0YOm5RyJ5AGDAdexh1ZG4Z7ObPWnxQhhAH4HPhYSplewSFhQP5xj8v/PiX2K4S4UQixRgixJien4fWR8yW9zncnWa76URtRH0+h6BVanRtL5nztdT3QCoa28YgQM7Z1W/1tStWoZbJ+Jcy/dgQBQAnphj5pDUrsg6i5H5R1SVha63H85bRVVrqhJDWe9V89wet9LcdayNWlLIY/S0MUd2vKhuXjKG0bTfuLvqbp22t8Nrev0J8VgeX3VDAIigdvxTEn79hz3n7vtVj2o8a/3NLNQinl61LK16SUP8s6yDiEEArwKe5OCbdXclgRcPwtdvnfp9zeSSnfk1L2lFL2jIsL3pVXRctUSYsUt1o00EgcHoc1x8GhP/OrP/g/iNDrMHZqg219/ZSi3hYfSOkuzyJEtWmxQXyEUEzomz6HvvVSQODMGIjz4INItXaFTn3ttFVXuuGwSeWHuBIcZZdDl8vF0nU1L4uhhdIQ9hYRbFw0htxhbUm6awGt71kArsDqaKPrFIJlWSpKezOll+7E9uYhr7/3Wvi/rYiqCufeK4QwH/d3pVtNJxPubOcPgSbAJVJKRyWHbgK6HPe4C5Atpax7ZccggHtZdONigQaiux6l1TmxCJ1gzxxtqUW1hCmtHfb03agaUMhVirS6/1WConCtoYT2xdBmHUr0DahHXsC56zRU6/rqTzwOXzptNSp7wUnOjcPB3Plf1fx8DZSGUMOMpM+8lP13nU6zt9aQeslMlELfdg3wNkpTA5ZfUtAPj8R2715mPfe5V997rfzfnkxVEbY7AMtxf1e2VRYlq4i3gfbA+bL8VrpiPgGuE0J0EEJEAxNwq0uD1JNeI1VcTsFfPwXWsqgp2kCzfpGa7HpwMscHpqXdd/3CTF1SwOnEvnmXz+asNeX3cMLoXzuCVIjQhaFv/i76+DlI1yGcu07DlfMiUmovqlOnshkK7F29koiVm+t0vrebp1eKTiHjhbPZ+eZQohfspPOgTzDu9X+KkEcbx1t0hHzdBuNdjdmZt9urZTm0WvajRmU9PDKREAm4hQo24PhfqZuApcBmoIOUMrPs+HuBh4AQ4FvgZilllbcNwbIe1aOqMDbBSMd+Kg/NCKzmoutey2TFA9u5amsfIlprc0mtdNF2rL9ux7oiA8e2wxg7NiXizv6YhySjhBi8OrfzcC77Bo0j+oFxRI6te3kOb5b2UIt+xbnnLPSJi1EsA7w2T5D6I52Hce6/CVn4HSJ0EPqWnyAMrWp8vhZKfsCJzdNv6DCU9re/SkjGQXY/fBUHrzqLR997lP05+2kR14JnbnymXuN7onl6dUQt3EnKVd+hhurZ8t0oins09/qcleGt125/+xDWe/aidA0l9Lu2KM28e+30Jh4v6yE80NSvrGG8kFKapZRhx22fSykzy/7OPO74l6WUTaSUEVLKcdU5a0FqhqLA6SNU/l6g4AiwdzRhmDa7HgCUzE9nX/tnOXTRNGzrsgg5px2NPh1NyLntyHtyAcWf/+V1G/SNotE1b6Rx4UH5DWRgRYADEaFvhL7Vt+iaf4i0rsGxIw1X/pc1Pl8LJT9OVgJmxxjZ8MXj5PbrTNIzn+Gc9Cb7c/YDkJWTRWZ2ZjUjVj2+L3Kg8s5pw4bF16Ka9HQa8ikx31ek6/M+3nztxlsaE/JtG9StVor7bcG1QVutCb1FTa+K+UKIBUKIR4QQZ3jCgQviP3qPVCktEqxbFFg/ilHJ2ux64DpURNHHqwm9sDMJ+VNoOucGoh4+k5DBbYm8dxDht/Sh6OPVPrHF3CW13g6bb7oeBNW+DQEhBLro8Rja/IMwtce170qc+65Bumom/vG301aREtAVFkL6G3ex77phPFu05oSP4ruz3633+L6gtGMjNiwbS0nnxrS7/Fuav7zS5y25vP3aDcOjsCxqBy4oHpSO82f/LwF7m5r+Yl8ErMZd1uN3IO94B85bxgXxDl2GqISEyYAr7wGQMCKO/YtzsRdoZ7nXtnYfjq2HiH7mPKR6aq6P61ARhtQmPrHF1LUdruwjOA9otWZd+WdSezlRQSpHGNugb72krNjuDBw7u6KWLK/Ruf5y2qpUAuoUlo7uxY4o4LjGILWJsvlbaehoEsamn6/myMXtSXz4V5Ju+wnh8E2XG1+9dl23UCxLU1ESTZSM3I79Q61e1zxDTeuw/SylnCCl7AdE4Xbg9gOTgGXeMy+INzCYoNs5Kn/OUajAf2jQJI6IQ3VI9v6sHUGxMa05zl1HwKEiFAU1vxRHxlFKF27lyD3fUzh1OWHjT/eJLaauqQDY/tHosqgoay0mA6t92n8BIfTuYrutlwIKzt0DcB56Eimrv3nyh9NWnRKwsmhaTaNsWlAaqiEGtn1+Efse6kPTD9bSfuRX6PKsXp/Xl69daWXE8ns7dGdFYL0lE+uj+5BqYEboaxxiEUI0EUJcjrtw7lvAFcBy3E5bkAZG75EquQcF21YHVjP4Jr0jMcXoNbUsqm8WQdj4XmT1eJnsCz8id9JC8ibOJ/+VxahHS2j8/XjMZyT6xBZju0SE2Yj1n/rltXhtWbTcYaOyij9BtI4SegaGNu4+pOrhp3DuHoi0Z1R7Xm2dtjtbjWKs8dpTtjtbjTrhuD3Ze7jlpVtOiYxVpwQ8nFdxtOZwzoEaLS96SmlYmf3lVKvEVASZkwez4/0RRCzeQ+cBH2PanVfz86ugsnM99dprapsI1xH6XVsMN8ZhfzGb0tG7kaUBFo0AatQpWwixCUgE/sS9JHoTsCIoBGi49BymotNLVs1WSO0VONEMRa8Qf27csa4Hik4bDmn0lGGEnNsO564jOHcewdChCWGn9cR0WjxKhNlndgiDHmOnZA1H2Mrqr9WyKGsQbSF0EehbfoIr/Dxc+2/GsbMLuubvoou8osrzyp22mihIC7IrVoKfvP/d2e9Saivl3dnvnqDynHRd1bGG9x98H/hX6Tik8wAm/W6l0U+rOFTwHjufGoc0VV5+prrxa0pl9pdzfL/LqpSYh67tgjUhktRR35LWbxpbvr2Mot4ta3x+RVR2rqdee21sE3qB+Y14lCQTtkeyKMmyE/JtG5RGDVdBejI1jbBFAi6gBCjG3XFAw9U3g1RHWBR0GihZGaDN4K05DrJXaafrgWI2EHpuKhG39CXmxZFu0cGZKT511soxd0vFnr4L1apBp8hdq5uqyzQGaSjoIq8sEyR0cgsSssYhXUXVnuepJdI92Xs8pvJcsvkPVj9xJXvuvJjGP66g09hnMRzO84idlVGd/bVVYhYMSmT90rE4I0x0OvszxBd/1lnJqcVenkIITPc2JWRGEq5/Stw9SLd6fwnYV9Q0h60l0B34DugKfA8cFUL8IIS4x2vWBfEqvUe6yNqmsG+rNqJQnqLVubEoesGeH7WzLKoWWDk41J37IqVEqmqFAgRfYOqaCk4X9g31a1PlDYQS6v5DDTpsgYIwtkbfejFKo8dR8z7Bsas7amn1ZWw84bSdnG9Wb5Xn8h/Iumkk6a/dQej2LNIufwrLpox621kZ1dlfFyWmtV0sG5aOpahnc+bP/KzKXqpVoeVenoaLown9pR0UqhQPSMe55JSulg2S2vQS3SGl/AC4FhiF22k7D3jRO6YF8TanjyhrBh9gUTZTpJ5mA6LYM1c7iiElwoypdyJqkQ0hBEJREMq/77t0qTj35uHK9v6FpVx4YF27pV7jeCWPTSlrrqJWH4UJ0nAQQo++8ST0iYtALcW5+wxcOa+c0PWjIurjtB0fnSrHUyrPo2f1YMNnj4Gi0GnMFGLn/1lnO+tqf32UmM64UJZ/M4xvexThLFNk1+b8htDLU3+6xd2DtLGBkvO2Y/9cO0K0ulLTwrmnCSEeFEL8BOTizmNrD7wEDPOeeUG8SaNW0La7yorZgeWwgXtZNDe9hPydJf425RjRT56LElZJj0xFYF26i/yXf/e6HbqocAxJLT2Sx+Zxp00Jc/8bdNgCEsUy0L1EGjYMV/a9ODNHIJ1V31jV1WnztsqzJDWe9V89QXH7BNrdN5VWb36HJ2X31dlfXyXm96vn4jKcuLoi1Zqd720VqKfGV1qbsCxph65vGNZxGdgm76/2JkHL1PSXejnuUh7rcEfXYqSUvaWUD0spF3jNuiBep9dIlW1/Khw94G9LPEvi8EYAZGioGbzrcBEFU5djXbXn2D5pd2Jbuw8hBMZOTSmesdYntpi6tce2Nt1vy7KVIkIAHVINjCWMIJDvOsBLRwaS7zoIgNDHom/1HbqmbyKLf8Wxswtq0aIqx6jQaQs7WPHBZfsrU3keyjsEVK8yrYnS0REbwaaPHiT7ov60ens2KfdNRSnxTG5odfbXV4lZ0flO1cXOXdUryL3da9OT44toPaFz2mK4Jhbb5ANYr8tA2jV23ashNeolKoSwSCmLfWBPvQj2Eq09GRsEd/YwcutbDobe0DA/xJXxVdeVhDQ2MnJhd3+bAoAru5CDQ9+j6aJb0EWHHtu/N34SLbY8jGIxktnqKZotuQND6xiv2lL43a8cmfAGzWe/jrFtfL3G8nRvUXt6LErEFeibv+XRcYP4hy/yb2Vp6bsMCLmZKyNP/D9Vretw7r0C7FtR4h5D1/gJhKi6eIGnepCONVYeuZtur+UcUtL84/kkvPg1xanxpL9xJ/ZmsfW00LeEL99L6qUzQUL6N5dS2K9+1wWtIaXE/swBbJMOoBsYRujXbRDRNSqU4VU83ku0IThrQepGQidJ06TA7HqQODyOg8vysOVpo6aXrkk4ruxC1MPur5N0lTnIJj1Fn6zGuScXQ3IjnBlHvW6LuXt7AGx/1y+PzSsoUaDm+duKIB4g33WAFaXTkKj8UTrtWJStHMXcBUObNShR16LmPI0zYwjSsbfKMf3dzqpChGD/2PNIf+suzJnZpF0xibB1nok2+YrCvq3YsHQsztgQOg79grgvNvrbJI8ihMA0oTkh0xNxrSimuH866i4NKuWrIPB+pYPUCiGg10gX6xYplARYK7aEEXGoTknmfO0km5pOj6f4uw1Il4rQKdg3HEAXHUrh239w+NovMPVKwNw30et26OObocRGYv17c73H8nQem9BFI125Hh0ziH+YWzQZtSypXcXFvKLJpxwjFAv6FtPQtfgMaf3b3daqcE6V42rSaQNyB3ZlwxePo4YY6TT2WeLm/OFvk2qFtW0MG5aOpbB3C1LGzqbl5CU+70HqbQxXxRL6UzLqYSfF/dNxrmo4+bJBhy0IvUeqOO2CvxcE1seh8emRmBsZNNX1IPyWPpTO3czhKz7l6MNzKHx/BXHTryRq0lDM/ZMIu6Ibwuj9ML0QAnP3DtqMsOliwKUdJztI3SiPrrnKSna6sFcYZStHFzUaQ9LfCEM8zszzcR68D6lWXu5Tq05badsWrP/yCQq7tCHlofeIf/Ubj4oRvI0zJoTN867i0Jg04icvJXnsDwibdnozewJ9/3AsS1IhQkfJ2dtwfNswbhAD6xc6SJ1IPUMS2SjwlkUVnSDhvDgyFxzB5dDGBTPknHbEvnkxGHXYNx7A1Kc1xg5NsFzYmejJ52Hs0txntpi6t8eZdQhntracI6GPQwYdtgbP8dG1ciqLspUjTCnoW69Aib4V9cjLODP6V9nWSqtOmzMqjM3vPcDBSwfS8v05tLv7TZTihlPAVRp17Hh/BHsmDaLRjI10HPoF+hztKO49ga6d2a0g7RZK6ZW7sL10UPMKUv9n3AXxOzqdu1XVyu8VHHYwVN5tpcGROCKOrZ8c4ODyPFoM8m4if00QQmBMa07jz68+ts+5Lw9nxlEcu46gHi0hdGQnDEneT1g29+gAgPWvzYQN6+/1+WqMrhE4D/nbiiD1ZNnkSahFU0/Y5wKWhuVwZRXVO4ViRt/8LR54+SUKi07tBBIRAc8//+9j60fX1kmIENGktML2VhFN3EWb72w1qtLnX9/7dbXjS6OeXU+OpbRtCxKfn0Hnq58h/a27sDWPq7Wt3iSvKI+p303l1otuJSos6t8nhCDr4b5Yk6JJvu4HOvefzpbZl2NNaVhiiqpQGhkIXZBC6XUZ2B7JQt1pw/x6PEKvzWLylTpsQoh7azqIlPJlz5gTxF/0Hqny68c6Ni4RdDtL23cZtaHlWTHoTAp75h3RhMMGHCulUfrzNgrfXIZ9Szay1IESbkLXNILS+elYLkkj/IYzvGqHsV1rRKgZmwcctvHjZ3tMLSr0jUEtRKpWhOL71l1BPINaVLFjUtn+k6nIWQMoqCDXtjY9SMupzumqaa/SKhGCA9ecQ2nrZqTcP5XOV0xi62t3UNgtueZjeJnq+nUeGdUBW3wE7S+ZSef+09n69aUUDEzwg6XeQZgVQj5tjS3RhP2Fg6iZdkK/SEJE6Pxt2ilUtQZ2Rw23271sYxAf0PUsFVOoZNUP2vuQ1gdDmJ7mg6LJ+PGwZsLdQlGw/raDo/fMRtc8kkbTrqRV5kRapj9C0wU3ETauF3lP/+J9O/Q6TF3beUR44FH0Tdz/BqNsQWqJVpdI8/p1ZsMXj+MKNdNx3HM0+mG5v00Cat6vs6h3S9YvG4ejSRgdhn1Bo0/W+9ZQLyMUgfmZFpjfScD1awHFg7ai7tVeu/RKHTYpZesabkm+NDiIdzCFQLezVFb9qASaKIjEEXEU7CwlL10bORhqgZX8F34j/IbexL17Geb+SQid+6soTHrCLu8KUuLK8X41HXP3Dji2Z+LK145SSuibAiCdlRRGDfKfRy2oXJmsVaetNKk5G76cSGG3ZJIfeZ/4V2b6XYxQm36dttZRbFhyLQX940m+/kdaPfF7wClIjePjCP0xGTXTRnG/dFxrtfGbUU5gZZkHqRe9RqocyRLs+Fub6/d1JWG4ewkmY442eosqEWbs6/ZjGdX1hP1qiR37uv0cHPE+5iHJiBCD120x9+wIUmKrZ19R8GB5jzKHDWeAtd8I4jGcey90q0hlxTUWteq0ucUI93Fw1CBafjCXdne94TcxQl36dbqizGz58Qqyx3ah1f+Wk3zN9whrgClIz4rA8nsq6KF4yFYcc/P8bdIxauywCSFihBBXCSEeFkJMPH7zpoFBfMdpw1UUnWRVgPUWDWtpJq5ruKbKe5j6tCbvqQUUfrKaknlbKP76HwpeXULes7+ii7EQ9ehZKBbvqz+MnZPBoMe6ZpNHxvOE0yb0bqWsdO6v5sgg/1WOqUh3D6y00K5WnTZp0LNr4rXsemQ0Mb//Q+ern8G03/fXprr265QGHTvfHc6eZwbT6OvNdDz3c/SHA6u2vq5TCJZl7VHamSm9ZCf2t7WRnlHT5u+9ge3Ai8BkYDzwGHA/cGlNJxNC3C6EWCOEsAkhpldx3FghhEsIUXTcNqim8wSpGxGx0LGfZOUPgeWwgTvKlr0yn9LD2shLiH39IpSoEArf/oPC91ZQ8O4K7H/vw9yvNdGTz8OQ0sgndihmE6ZOyVj/0lAem74xoCAdQYetIRMRUbv9tTlf3/wtdC2/Qto24tjZDbVwfoXH1sdpK1eL1nR/rRCCg1efzZa378W0P4fOV0wi7B/fdkaoV79OIch6oA9bZ1yMZe1B0vpNJ2SLdm6IPYHSzIDl1xT0wyKx3rUX6/17kS7/LgHXtKzHC8DnwF1AATAEKAZmAB/WYr79wNPAuUB1UpsVUsp+tRg7iAfoNVLlg/v07N8Bzdv62xrPkXh+HH89s5s9P+WQOsZ3tc4qQ98ikpjnz0cttuPMzEXfMhIl3IwrtwRZ4Nt2KeaeHcif9j1qcSmKpRYKOC8hhB70zcC5z9+mBDQPPlix4vLkshl1paKxj99f3/l1kaNQzF1x7r0MZ+Z5KHET0DV+EiHcwqlbbilLsbr5RKdNKJJp1k+OPa6srEW5irTSshceoFyMkHrbq3Qa9yw7Jo0n5/w+Hp2jMiZdN6neYxy5pD22VhGkXjyTzgM/Jv2rSygYnFh/4zSCsOgImdkG2wP7sL9+CHW3jZBPWiMs/hHn1TSUkga8Kd0yOxdgklJmAw8BT9Z0MinlLCnl90CwKqZG6XW++44r0NSicd3CsbQwsWeOtu4CFYsRXUwoRV/8zeHrvuTIjTM5cvu37G37DHlP/+wb4UHPTuB0YVu31etz1RRhaFVtT8kg9aM6h8rf89fEPmFKQZ+0AiVqnLsX6Z5zkM5soPJ8eKmemKN7fFmLiqju+fpS2qZMjNClLSkPN7zOCEWnt2DDsrHYm4XRYfgMGn+8zt8meRShE5hfboX5lVY45+ZTfNY21IP+6U9dU4ft+HWkbKC8CEsR4K1wRTchRI4QYpsQ4nEhRLDIrw9okgit09SAWxYVQpAwPI59vxzFZdPOxdC6MoPD47+k9Kd09E0jMJ+dQth1vYiZMhz75mxyH5nrdRtM3VJBUTSVx4ahZdBhC1IjhBKKvsVH6Jp/hCz5w71EWrykRudWV9aipmUv6otbjHD/v50R7nkLpaThNCa3JZYpSAcm0PaGOcRP+A3UAFOQ3taYkG/aoG6xuhWkmzywNF5Lavqr/DdwWtnfvwNPCyGuBV4HvFGQZQnQCWgMXAJcCTxQ0YFCiBvL8uLW5OQEWPdyP9H7ApX0FYLcbH9b4lkShsfhKHKR9bs2+saphVYKXluKLs5CzCsXEjV5KBE3noHlws5YRnUl8p4BlC7a7nU7FEsIxvZJHnPYPIEwxIMjUzO184JoH130OPRJq0AJw5kxpEbnVFfWojZlL+pLeWeE3Q9dScyiv+k0ZgrGAw1nMcoVaWbLD5dz8LqutHz+D1Ku/g6l1D+RKG9hGBGFZVEK2FWKB23Fuci3PkdNHbbHcOefAUwADgNvANHATZ42Skq5S0q5W0qpSik3AJOoRNwgpXxPStlTStkzLq6G2axBqqTX+SpSClbPDawoW4vB0egtOs2U93AdLMS2IoNGH1+FoXUMQjnx/bYu3ompe0uk3fuyefNpHbGt34Zq04YoQxgSQFrBpY3/qyANA8WchiFpDSLioiqPs350bbVlLepS9qLeCMGBMeeyZeo9mDOzSbtiEmHrd3lvPg8jDTp2TR1Gxv+GEPfNFjqc+zmGQwGmIO1ucStIWxooGbEd+3TfpdnU6BdZSrlGSvlb2d+HpZTnSSkjyhwlX5Q8lkBgFQfTMK27SBonSFYF2LKo3qyj1Vkx7Jmbo4nIjSG5EbLUQcmC9GP7nPvyKPrqH7Iv/Ij8V5cQcVd/hNH72QDmnh3B4cS+fpvX56oJwpAIUGXj7yBBKkLoItC3rL7X56z3t1ZZ1qKuZS88QV7/NDZ88Tiq2UjHsf8jdt5Kr8/pMYRg/31nkP7lJVjWZdO5fwAqSOONWH5PRTcoHOuNe7A+nuWT35Qa/RIIIRYBF0sp807aHwF8L6WsUfy5LA9ND+gAnRDCDDillM6TjjsP+FtKmS2ESAUeB2bWZI4g9UcIt/hg/vs6SosgJMzfFnmOhPPj2D37MEf+KSKuW7i/zSHykTMpeHUJuQ/PRTpcKJFmlDAThpRGRD81FGOX5kgpEcK79yum7h1ACKyrN2E+rVO9x6t3b1FjIgDSkQGcXm97GiLeVnFGRFQ+fk04psI8CSHg7berP1+Iys+vCVW/P6La8Xc5VlRZ1qJeZS88QGnbFqyf8Tipd71JuwfeYe+uA+y97cJT3iBvqljrw9GLU9kUH0HqRV/TecB00r++NLAUpJE6QmcnY70jE/tzB1EzbIS8n4gwey/QUdNb90FARVU8zUBtukZPAJ447vHVwFNCiI+AzUAHKWUmcCYwXQgRhlvk8BkwpRbzBKknvS9Q+fFNPWsXKvS5WDtJ+vUl4bw4EO6uB5pw2O4eiHlQW+x/70OJDEGEGtA1i8CQ3OhY4VxvO2sAusgwjKmtsa7eCFzu9fmqQxhau/+wN5zlIE/jbRVnfZ2+SlWYZfvfead+51dHde9PudMonYdw7rsSWbwIJep6dM3eAMxMiFt7wnknN473RNmL+uKMiWDThw/Q5snptHp7NiG7D7DjmetRzf/+HFfXvN2fFPVszoZl40i98Cs6DJ/BrrfO49C4rv42y2MIg8D8djxKkgnbhCxK9toJ+aYtSpx3VkWqdAWFEN2FEN3LHqaVPy7bTgNuBLJqOpmU8kkppThpe1JKmSmlDCtz1pBS3i+lbCKltEgpk6SUE2VlPUiCeIUOfSXhMYFXRDekkZEmvSPJ0FB5D1PXFoSP74XlkjRCz2uPqWsLn3Q5OBlzz47Y1m1F2v3/VRO6cNDFIR3/XYctiGcQ+sboExaixD2CmvcBzt19kfbdpxyn2c4IRgM7nrmejHtHEbtgNR2v/R+Gw3mA71Ss9cGWEMnG38eQPziRtjfNDTgFqRAC04NNCfm8Na6/SigZkI5ru3fajVX3a7wGWI07h2xh2ePybRXwCG5BQJAAQ6eHnsNU1vyk4PT/77dHSRwRR87aQor2+aeHX0VoIafOfHonpM2ObYNn8tjqW95DGJOQ/+EIWxDPIYQOfZMp6FvNRtp34tjVA7Vw3inHadVpQwj2XzeM9NfvIHTnftKumIRlc4ZPVaz1wRVpJv37URy8vptbQTo6ABWkl8UQujAFmeeiZEA6zuVFHp+jOoetNdAGd8L/6WWPy7cWQISU8iOPWxVEE/QeqVKUK9i0NLD0Hokj3G2ftNRb1BfLntVh6tHRncf250Z/mwKAMLZF2n3bridIYKNEjMTQ5i+EIR5n5gich55AyhPz1DTrtAG5Q7qz4bPHAGh84zMsX7vEtyrWeiANOna9dR4Z/xtC7KwtdDwn8BSk+jPCsCxNRcToKTl3G46vjnp0/CodNinlHillhpRSKVOK7jluOyBP/qQHCSi6n6NiDJGsDLCuB1GpoUS0DdHUsqgW0EWGYWyXWJbHpgGMbcGxF6k2nAKiQbSPMLZB3/oPlKgxqIcn4cwcgXSeWO9My05bSWo867+cyBu9zEjniT/BWo6yAccUpFu/vITQ9dl07jct8BSkbUyELklFd7qF0mt2Y3v2gMdWUGqcGVem3LwNSALOlVLuFUJcD+yWUv7qEWuCaApTKHQ9U2XVjwo3vlJz9ZbWEUKQODyOjW/vw1HkxBAWbKJRjvm0ThR+vQBpdyCMBr/aIoxtARUcu8GU6ldbKsLfKs6bb6783HfeqV7FWd/nq6O696c6FWd1z9dH5SqUUHTNpyFCeuPKfgTpzELoY084ptxpO1mMoAUcjaL4MzUKx+HCE/b7UsVaH45elMqmVv8qSLd+dQn5Q1r72yyPocTqCf0pmdIb9mCbuB91tw3zmwkIQ/1+RGta1mM08A7wAW4FZ/mVXAc8CAQdtgCl9wUqf87RsesfQZtu/s+z8hQJIxqx/rW97F14lKSLG/vbnGNYV2Sg5pUSel57v8xvPr0TBZ/+iG39NndttnpSn/IewpgMgLRvR2jQYWvoKs76Pl8d1b0/1Y1fnVNY3/dHCIEu5maUyCsRushKj7N+dK0mnbZJN0wGKWn59g/Ev/UdBd1TSH/tdpwxDaOAfLmCtP0FX9F+xJfsmnoeh8Z29bdZHkOYFEI+TsSWZMI+5QDqHjuhXyYhouoeIKipBPBB4AYp5T3A8TXTVgJd6zx7EM1z2jAVRZGsnB1YatFmfSMxRes10/WgnLxJC8l9aI7f5v83j22Dx8asq/hAGFMAkDZtFPMNEphU5ayVo9klUiHYd+sFbH3xFiybdpN25WRCdtS4cIPfsSVEsmFxmYL0xsBUkJqfbI75gwRcSwopHrQVdU/dUzxq+iucDKyoYH8R0DDc+SB1IrIRtO8beOU9FL1C/NA4Mn86gurSzgUiZGgqjvRDODI8m6xaU47VY9OA8EDoY9ylPexb/W1KkCDHnDb7H4uw/fYT1jlfI53ebxtXE46c14tN0x9BsdrpPPppopb6ogGRZ/gvKEiNY+IInZuMmuWguH86rr/qJrao6a/wfiClgv0DgJ11mjlIg6H3SJU9GxUOBliFhYQRcViPOMhekedvU44ROtS99Fd6XLsqX2M+vRPWdVtRrf5P9hemdkhb0GEL4n+k8yiFT36LbdFc1CPZqNlZFD37ELK0xN+mAVCUlsT6LydiaxFH+1tfoennP9d8/drP/CcUpIMjsCxpB2aF4iFbcczOq/UYNXXY3gNeF0L0LXvcSghxLfA8UIP00yANmV7nu5VIgaYWjT83FsUgNKUW1ac0Qp8UQ+lP/nTYOoPdgW2d/5cihTEVafPfe6ElJJIi/Xb2WKazIfqeKo/9rVk3H1n130C68nAduA1p34G+yU5CLh1L6HX3oGuRgHOndm4o7M1i2fDpY+QO7ErSlM9JmvwpOBtIMYdyBemMSwgN0B6kuvYhWJamonQKoXTUTmyvZ9fq/Bplv0kpnxdCRAI/425H9RtgA16UUr5VW6ODNCyaJkFiZ7da9MK7G8iXvwYYI/Q0HxhNxo85nPFssr/NAdw5DyFD21M07U9UqwPF7HulprlnR9ApWFetJ6RXZ4+MWVfxgTClQt6HSOdR9xKphqhvL87qOFVlKYBkjNHhnP3ZbcDLZftORmJ2tgChgqzgnlyobIt4AXdqcuWqNW+rOKt73tsq3NrgOvQEaumfGJL+QOgisX50LdJVhCv7PvSde/jWmGpQLWbSX7uDhFe/ocVH8zDvzWbrS7fiirD427QacfTiVDa1Cif14pkB2YNUaWLA8nM7Sq/dje3+fbU6t8ZyBSnlY0KIZ4AOuCNzm6WUni/lG0ST9DpfZeazOvIPu/PaAoXEEXEsu3sbeVuLiWqnjQtayNBUCqcux7p4J6Hn+l4dqYSFYuzQRht5bCa3WlbatyD0fas52rd422moTGVpz23KiL0FzK3U2RKccXgOZ5StfdiVoxQaNpNvWEeeaQ1HTSvYbNgKPFTl/NWpNKtTeVb3/lT3vLdVuDVFLVqEmvs++qSVCH0TwN2ZRC2cDc6+6BPb+tagmqBT2HPfKEqTmpH05HQ6j36aLW/dgy1eO4r4qig6rQUblo6l/YVfu3uQBpqCNFQh5KskbA/vg1drfl51vURDhRBvCSGyhBCHcJf1yJBS/hl01v5b9L5ARVUFq+cFlvggYXgcgKaWRc0D2yDMekrn+3dZ1LZhG2pxqd9sgOMcNtsWv9rhS2zKYdbEXl3lMYKapycY1Rhibf1IKrqN7kemcdb+dM7bW/VSjF05UuXz/yWkcy8i7GwUc9q/+0qWIwt/RBjisX1/t3ufBvPFDl3Un80fPIDhSAFpV04iYo12lm+rw5YYxYbFYygYlBCYClJFYH6+Va3Oqe7X9ylgLDAX+BI4m2DO2n+SpK6SRvGBV94jPCGE2LQwTZX3UEIMmAe39avDFtKrMzhdWP/2s6NkSAQRgrRt9q8dPiLHtIRFzdLIsnzt1XlMatWRlp9aNmVlowvYHzILFbtXbdE8UgX13wK1auEc1Nz3kbIUXaOJCMVI6YdXH2sv5zp8EOfu7f6y9hQKTktlw4yJOKLD6HDd8zT+bqm/TaoxrkgzW2ZfzsHruroVpFcHnoK0NlT363sxcJ2U8kYp5Z3AcOBCIURgZZ8HqRYh3OKDf35RsAaWeIfE8xuRvSKf0hzt/DCFDE3FufMIjm3+cSRN3dqDXo91lefKA9SlHpsQCsKU+p9w2DItn7C8yRD0MpxBB1b71ZY2BXeRZ1zNn40vYX7LlmyMeoAivXacEF+iRI5COg7g2DMcR8bZuHJeAMWEvulrCH0jpHQhhA7rR9eiHs3BsWoJJW9NwTp7hr9NP4Y1oQkbPn+cgtNSaTvhQ+Jf/hpU1d9m1Qhp0LFr6jAypgwh7pstdDj3c/SHA+xHqIZU57C1Ao6541LKP3EXzm3uTaOCaJNeI1XsVsHfCwMrypZ4fhxShcx52lkGChnqXgos8VOUTQk1Y+qS4tECunVFmDohrf7Pp/Mmu8Pe5e+4a4mzDmLQgTVEOrr41Z5OeS9yTlYmvbPnEmvtz86IV/mlRQrLG5/DgZAfkASO+Kg6hGLB0HYzStg5KJaz0DV7A13jZxHGRKRUKY9fSMcBSt8rwXVgLyFX3oBz+2ZKP3/Xz9b/iyvSwpa37+HgqEG0/HAe7e55C6XE/6V7aoQQ7L//DLbOuBjLP9mk9Z9OSLp20lh8RXWiAx2cEg931uC8IAFIx36SsGjJqh8V+lzUMO7OakJct3AsLUxkzDlMuzHN/G0OAIbWMRhSG1M6fwuRd/b3iw3mXp3Jf2cmrvwidJFhHh+/pipAYeoI+Z8iXXkIXZTH7fAXJ77+m8o2mF3DXpv1ValWd76CnqbWYTS1DsOqO0BG2AdkhL3LqsYXYHG0ITRyHSX5pwp1PKWS9bYKtzYIIdDF3nXssZRq2X6l7LEDad+OK/cdFOcIXOvexXL3BxS/MAHb4gWYBp7re6MrQBr07Jp4LaVJzUl8fgadxkwh/a27sTeJ9rdpNeLIJe2xtYooU5B+TPrXl1AwKNHfZvmM6hwvAXwmhDjeDTcD7wshjlULlFKO9IZxQbSF3uBuVbVmnoLT4X4cCAghSBgex7bPD+K0utCbtbHiHzKsPQVvLkMtsqGEmXw/f+808qd+hXXNRixn9vbImMeX96ipClCYOwEgrRsRln4esUML1LfXZn1VqrU53+xqRmr+46TkP8yB0O/YGf4qA74Mw+CKonXRrSQV3IlZbVI/g+phny9RC+fgPHg/hjbrEIr7eymEAUL7om/2Fs4Dt+LKPQPbJ9cT9ogBNc8/XUsqRQgOXHMOpQlNSLn/bTpf8RTpb95NccdEf1tWI4pOL1eQfkWH4TPY+fZwDo9Jq/7EAKC6ta2PcXc5OHLc9hmw96R9Qf4jDLhcped5KiU+ltZ7m8QRcTiLXWT9lutvU44RMjQV7C5Kf/VP7pCpcwrCbMS6yrPLorXNZRMmdy04aQvsZdGGgIKBFiWjGJD9BwMOrCDOOoRtEf9jYYtE1kXfToku098meh0lfAT6lp8hFBPSeRTp2P/vcxEXom/2DmrhLKQzB+tH1yIitRm9yhvQhY2fPYbU6+g0ZgoxP6/xt0k1xtY6ig2Lr6WgfzzJ1/9Iqyd+bzBdHepDlQ6blHJcTTZfGRvE//QYqnLPNCcRsf62xLM0HxSN3qJjj5bKe/RtjQg3+U0tKowGTN07YF3p576EhlagRCCt/s+nC/IvMfbe9Mr5lrP2p9OqeDQZ4e/xc4s2rI25gWL9bn+b51WEuQdSOnAdfR21+JeyvWXLo2oROA+CEgKAbdpYXFl7cPzzJ/alP6Pma+emsCSlFRtmTKSkXStS736TFu/PaTCOjyvKzJYfryB7XBda/W85yWNmI6za6O3qLQIrezxIkDqiN+tofUEjTdVSEgYdIWelUDo/3W92hfROw7FzL87D/vuREUIgzJ2RtsBx2Ir1gdOCOcyZQrejH3B21g4SC29ib9in/NI8hbUxNwZsxE0IgRAGFHM3XAfuQC38ESEE0nEAHHtB3xSkipQuXPlfUfzqC9hXLcG5dSNFzz+Ka/9ef7+EYzjiItn00UMcPq8XCa9+Q9vHPkDYG0bpDGnQsfOd4ex5ejCNvtpEx6Gfo8/RRm9XbxB02IIEKWPItA4MnNre32acQMh5qbiy8nGsP+CX+c293bkhnizvUReEKQ1pXacph7o+bIma6G8TPE6oK54uuW9ydtbOMsftY35pkcz66DuxKrXrmdhQUCIuQN/iU5z7b8SReQnOvRehFnyJLvpWhC4cNf8zXAduQdfkRXSGDSjKPxj7n4NjzTJNfZZVs5HtL9xM5m0X0nj2cjrc8CL63MLqT9QCQpD1YB+2fn4RYX8doHP/6Zi3BWamVtBhCxKkjPLCl1oiZKi7NVXJT/4pYGtMbY0SEebxZdHx42dXqvaraL8wp4FaAI49HrXDHxTq09kXOoPQyIp/EI/vtVnV81olxNWCLrlvclbWdloVjWF3+FR+bpHE5qgJOES+v83zOErESAyJv6NEjEQXex+65u+hhA9FLVmJ6+D96BpNQhdz0zEHzbmmKerRHO1db4Rg360Xsu35mwndtR/DkYaVqHzksg5s/Plq9AU2OvefTsSShn+tOBnhSy9fCHE77s4JnYEZUsqxVRx7D+5mdyHAt8AtUsoqi8b06NFWrlz5ksfsDRJEC+zv/RrCpKPZ4tv9Mv+hu57FtmknLX9+z6M/MrVpBq+WrMC5uw/6Vt+jRNTsvFtuqbwsRnV9Mj1xfmVlS0Ii8xn8RVPOzdpTbceBuoxfXhZFK83Ti/Tb2RI1kSzLlxhdsbTLf5zWhbegYPSdET5GSheOHR1Rws5G3+yNY/tV6wZchyehhF+A5V7t1rJTSmyoob5XpnsC065c2l/wFeZduex8ZziHr9G2gnSscexfUsqeNTnW1xG2/cDTwEdVHSSEOBd4GDgTSASScLfJCtJA0FC0v8ETMjQV26pMXEf8U93b3DsN14HDODMP+mV+KFeKCqR1XY3Pqa4shrfPr6xsR2l+JC1LrqqXs1bV+OX7tdI8PcyZzGk5Mxh04C8i7d3YEHM3vzRvT1boTCSBeaGQtnSEEoYu9v5/9zn2Iwu+B7UQJaSnuzNCQR7ObZtw7tBWr9yG6qwB2JKi2bDkWgr7tCL5uh9pNWlJwPwg+dRhk1LOklJ+T/WlQK4FPpRSbpJS5gKTcUfmgmgUlxPsVigphP07/i3uGaT+hA5rD6qkdIF/GjeH9HZX3S9dWXNnydMIXRgY26Ja//GbDZ6kdeFN/jbB50TZu9Pn0ELOyP4JvbSwutEoljbpR67xT3+b5nGEMAASdJEASPtu1LzpqEU/oYu9B/TNcR1+lqIpr2Jb8D2lX35A6cxp/jW6Hlg2ZxCxcjMxC/3bUq0cV3QIm+deyaExabR6eiltx/2AsDV8BalWc9g6Asf/OqwDmgghTikmIYS4UQixRgixJienYa25Bwq/fqLw0hg9N3c0clVjI89daeDr/+k46p88ea/j62RhY8+WKI0slPopj02f2Bxd01isK/znsAEo5q7IAHHYouyn+dsEvyAQNLEOZfCBtXQ98h7Fhp0sbtaLv2LHUKrL8rd5HkOYUkDfHGfG2bgOP4tz31WopX+ii7sfEToA16FHUUtXoYt7FJ1lG2H3Tca1Ix3ntk3+Nr12OF00+3QhHa97npbv/Uird36g0zVT/G0VANKoY8f7I9jz1EAaf7GRDsNmoD/SsBWkWnXYwoDjs1PL/w4/+UAp5XtSyp5Syp5xcRrPxg0wVs5WGJtg5JMJeiLi4LapDj4/aGfM007W/abww+va6BhQX1SXxOVQcdlVCjOtPk8WFopCyLmplC7cinT5viWYEIKQ3l2w/rkR6cGG0bUuoGvuBo7dSFeex2zwF4L/dghaoCOx6AbOytpOcv7DZFm+4pfm7dgaMQUXVn+b5xEMCT8iwocjXYdRIq9C3+Q5lIiLUXNeRDqz0UVdgy7mBgBsM25BlnYBVbt5bScjHE5avjeHVm9+x/b/3Uj61HtYN2syUido9N3S6gfwBUKQ9Ug/tn56IeGrsujc/2PMOzTWeaIWaNVhKwKO977K/24gOuPAJ+8Q/D5D4ZzrXHycaefm1530OFdiiYQe50oufcDJn3O0+vGqOdtnHOT36zfzVeeVfBj1OwsuW8+6V/ZQevjkFrveJfS89qi5pdhW+Uf5ZO6dhppfiH3LLr/MD2UOGwRMlC0IGGQ4HfP+x5n7t9DYeg5boh9jUfNOHAyZ42/TPIK+8ZPom76ELvYOhKkd0r4LtWQpSugglIiLjx2nlqxAlizB/utoP1pbO5rM/J1mn//M1ldvJ3dQV1STu1eh1OkwaKwkyJHLO7Jp4Wj0uaV07j+d8OXaqYNXG7T6i7oJ6HLc4y5AtpQyMIurNECyMwS71ilcNfHUO8KCHFg6U0fPYWqDzfXM+PEwnyQuY/l921CMCr3/15ard/elx2Otyfgxhw1v+vYLbz47BXQKpfP80/XgWD22Ff6rxyZCyhy20rU1O76SIFZNA6T1Pb/yshye+VJUV/ajIZUFsTiT6HV4Fn2yf0ZgYGXj81nRaERAFRgGUPM+Rzr3oYu97dg+ad+J6+A9KLF3o4R0p/TDMX60sGaEpmeS+MKX7HziWvL/3959h0dZZQ8c/553ZjIlvYfQO4SmgAoiIiqKXddeVlndn669rK66dlyx7dp7XUXX3dW1i12UIlhQitKkJhAghfRMn/v7YybUkJ6Zd+B+nicPyTtvOTOknLnvveeMHRLeKELK98uQYJCqA81VzxKg5uDuLJk9hUCGkyFHv07Wv+Ps9jPRL+thJdxw/g6gG/B/QEApFdhlv8nAP4HDgU2Ey3p8r5S6qanz67Ie0RMMwumpCTyx0Ed293CSVl0mFC4VFs00KPxVuOKZAL2GxV/G5i7xMfuqFaQPTuSAO/rs9njhJ2XM+8tvnLl4bFTj2nTk04Qq3HRdcF1Ur9tg48lXYclKJ++Fjl2w3ZryHr4VXTESD8fabXqHxtDZFIpPuuaT7T2c0WWvxzocUwvhY3XKY6xIvYuQ+OlfdRMDqm7CgiPWobVbcOtzKO9SrF0eAUAFSghs+D1i64ol83rEUbBtX8eFr8QoyuZlvzeXrBnzWfbsn8MrMEVwri4m7z9fYd1aw7q/nIU/x5w9VK1b3Qw8/S1SZxdSeOcENtw8Lqar5Mxc1uNWwE24ZMd5kc9vFZEeIlIrIj0AlFKfAA8AM4H1kY87ohyr1gSLBc69M8g9p9q48TAbr91hZfodFj55wYLVBlc9F5/JGkDlqnrKF9c0mqx5K/2s+6iM7kdnRn3xgeuYwfiXbCJQVBnV6zZwjhmB96dlhDxNlkPsVOIYScizIGbXb6s662q81s1keSbEOhTTM0igf/X1HFG8nC71p7Ai7S6+yh9KieOzWIfWbmIfTKjiWYKl9xPc+hz+NQci1kyMjMt2StYAPC9dEKMomyeBABiRJEeEpCVryHl7Fq4VRWw+90jTJmsAgQwnS2ecTck5Q+lx5zf0++OHiC8+5g5ao3kxpdSdwJ17eDhpl30fAh7q5JC0djjluiAjjwpRsl4oWiYMn6gYNCZEl76xjqx9ckanUFPooabQg6tLAt5yP54yP1uX1bHhy62U/ljNxBcKor74wHnsYCpu/oj6j5eRcnF0R/cAHGNHUD39A7w/L8c5dkTzB3QCcY5C1c5AheoQIzEmMbRFQ+mKdO9BMY4kfjiDXTmg7A161l7E4ozL+Tb3aLrWncmwiodxBLvEOrw2MRLHY+35CcGyBxBLFkbqeViyb0eMxosIe166wJQjbZXjhtHzkbfode/rGB4fCaWVKJuVostPpmb//o0fFAyBxRyzsJTdyqqXT8TbJ53uf5uNvaiK5f85lWC6M9ahNSmqCZu2dzEM6D1c0Xu44qATdn4sMkoelywJBqNu6c2M43/GlmIlY0gSnlIf3qoAqf1dHP7yEDKHJTV/og5mG5SDtXcG7hkxSthGDyFhUG+UN7oLLnZkOEYSIoTyLERc42IWR2tVJfyEEXKQ7B8S61DiTo7nSCYWL+a31PtZmTqNLc6PGVJxH71qL0FMOw17z4zECYjr4EittuY1jLSZKXHz5WWw+D930OXVzzB8AbacNgF3n3w8vfLCOygV/jB2+P+xGKAUhsdHyGmCwrwiFN1+KO6+6fS75COGHfoKy947E28f844ORnUOW2fTc9ii76aJNq55yU9e73DxXMMSv4najkJBRfniGmrWeahYVkdiVzu5B6aSPji2ozrl17xL7cvf033zXRjOlv3Cjwctncem/Bvxr+yGJe9RLJlXdXJUHWduziT8RgWHbf4x1qHEtVrrbyzKuJRS55dkeMay39bnSPEPjXVYUWOmpA1o9J25+AKohO1jQa4VRbhWbcS5ppjEZetJXFHEorfuIpC+W5WumEmZXcjA094Eq8Gyt8+g9qCuUbu2meewaXuZoy4MYo+MIlusO//sBgNQXgylhbGJrT0Mi5C9fwp9Tslh1F97M+iC/G3JmlIq6vPXGjiPGYRy+/F8vSom1+8sLa7JZs0Hax7KHV+JT41tqR5d6wBJgf4cXPI5I8teoda2kpldRrI09ba9pnbbrpS/CP/6E1D+cFFh081ri/zCz353Dr3/Fl4IpBKsuJYX0vtv0xl49eP0ePQt0uYspq6gJ4krijB8fpRJbo02qB7fI7yCNMXO0COnk/nm0liH1ChzvWpa3Dn89yHS8/b8+IJPDZ6/Lj7vvL8z4UfcJeHbf6Hg9iRNRKI+f62BY0JfxGWLWdeDWBMRxHkAIU/8JGx+qcFjLSbZPyjWoewVBKFH3fkcUbycbnVnsTLtb8zM359y+5xYh9bhlHclqv5r/GtGE6qfB5gwaQO2HjGS6pHhuWvi9dH/5udJWbCSddefyfKnrmX1XReSvHA1hsfHwrfvJpiSCAFzTfT3DMhkyewp1I7swsBz36HrA9+argepTti0dvPt4c2txQpDxilWLzRYOjf+7pMOPC8PFQr/wBqWnZM0T7mf1f/bwpYfqvZ0eKcwHDYch/en/uPlMRvlizXDMRq8y1FBcxXn3JOGWmKJgT1MxtbaxB7KYlT5q4zd8glBcTM7bzyL0q/AL/HxfdESRtIRWHvPB3ERWHcYwYpwv1GzJW3BZBflx44BQNkTWH3nBUggQPYH4SSz9z3TyX1zJov/fTv+7LTwQdZwJxzx+WMRcqMCWS5+/fRcSs8ooOetM+l76QzEb57EUidsWrvderSNnz/fnsx462Hpt8Krt1p4+EIrZUWw8of4+1Yr+L9uuPK2T47dMUGyOA3cpX6+vy36hT1dxw4muL4C/69bon5tMxDnaEChPD/FOpQWqbeuA8AV6BXTOPZWuZ6jOaL4F/pUX83a5Kf4Kn8oWxyfxjqsDmM4hmDr80O4B2nxhQQ2XYNSAdMlbduEQtSO6MdvD/yJ7A++Zdg5d5P1yfcs+u9deLvnAGC4vfS99UX63fwcg658jKQlseugsivlsPLbqydTdNM4cl9ayOAT/4Ol0hy33OPvr6hmOpn5ik+et/DNvw3uOM7GBT0SuPUoG7/MMhh3aojnVvg4+Zqg2UaXm+WrCfD1JcvYOHMroaDaaYTN6jQYcnFXKleEa7ZFk/OYcBXxve22aEvnsYkz3DhduX/ozHA6jNsa7orhDHSPcSR7L6tKYnjFI4zfMgeLcjEvdzI/ZV6ETypjHVqHEGsG1p4fY2RcQ2jrowTWT0YFtuJ56QLzJW5GeDVo3eCeVI8eQNKSNVQcOgJvjxwIBElavIb9Tr4Vx8YyavbvT/WoAQz5w3041xTHOvLtDKFo6mGsev54Ur5Zz7AJr2BfH927KY2GFesAtPh3whVB5r9n8N9pFvL7K25/38/btT4emOXnlGuD5PaKzzIfCclWimdV8MHkn5lz1Qo2fr29abCIIIbQZVwaG2ZWRDUua9dUEvbrSv0McyRsO448dmRz+D0RazbYeqLc33f6tTqCx1KMKCv2UHasQ9nrZXoPZmLxzwyoupmixFf4Kn8Im50fxTqsDiFixdrlYSz5L6PqZ+NfcwAhT7i9kumSNhGy351DzjtzWPn3y/B2zcKo8+BaXUzfO16mev9+/PryjWw5YyIbLz6BrRNH4vptY6yj3k3JBSNY+tHZJBTXMOyQl0n6MbZJpU7YtHYrGKcQA55c7OeSRwIUHBz+Ax4Mgt8XXi0ab8lag5zRKYy4tgeZI5KYd+MqPj9nCeVLaqnb5KXos3Jq1rtJ7h79ljnOYwbhnbeO4Nb6qF97R54ffqHyiTfY/Mc7KDriIrb86W7c8xehOnleiuE8kFCcJGxeSwn2YHZc1gyLRxYcFFRO49DN80kIZTA/53h+yvzDXjPaZkmfgrXXN6DqCawdQ6j6fcB8SVvpyYew8L17KD/6AAqvOY1QooP+Nz+Hp0cOq+67ZNt+9uIyUhasMN3K0QbVE3uxZNYUQk4rQ46YjnN5WcxiMecrpMWdAQcofvgo/O0UjMzRtFjAlhBefNAg3m6L9picyaY5lQy5uBtHTh9K2qBEPjj6J76+ZBm/PL2B7ANS6PO7nKjH5TquAEIK9yexaQZfP3sBG469jC2XTMX78zLs+w0i8/ZLcYwcTMWD/6T2o1mden1xHgj+9ahASadepyP4jDIS9Oha1KX7RjNh048MqLqFosTpkbltn8Q6rA5huMZg6/MjkjCIQNHJBEvvQSlluqTN3Tc/3OEAyHvtcyQQZMWjV2573FLrJuOLBdQO60Pt0N6xCrNZ7sFZLJnzBzbcOh73wMyYxRGf9RY007n7U//2emwWKFwqLJ8v/DrboHiVUDAuxDEXB8nbvT2nqfU8LovZV60AIG2AiwNu78Pwq7pT9PlWAnVBuh2ZEZO4EkZ3w8hJwj1jGUnnjIzqtYPlldS+8yWuww8k4/opOz3mmjAaIyWJ2ne+JPmUI1p97gsvfK9FRXTFGW7xpNzfI8nHt/o60eQ3KrCFzFs9fW9mwU5B5d/oUn8yP2VewLzcY+hZ838Mrfg7NpUS6/DaRWxdsfaeRbD4/wiW3IryLMbS9WXztbOKjJwpq4Wa4dv7Fhp1btK/WUTGzIWUTxqFLy8Da2Ut2e/OIeSy4+mRS9WYgj2dNer8OYlsvOHgmMagR9i0DtGQrP06R7hlko0bxtt471ELoSAcclqIrcXCtNNtbFkX0zBbzZ5mI//QdCqW1QGgQgp7mo1+p+cyaEo+Sd223w6NZpkNMQycRw/E/dkKVJTrGXl/WYV/bTHp1/6+0Tlryu3B2jW3U2MQ50jAQqj+u069TkfwG1XYQmmxDmOflu4bzWGbFtC/6i+sT3qRr/KHU2r/OtZhtZsYTixdp2PJvZ9Q9ZsE1o5H+YtMN9IGIMEgSb+sBcCxfgtd/vUlOe/OpuqAQWw+50hy/vcN/f76PF1e/xznmk0MuvwRsj6cF+OozUWPsGkdpr4G/vd3C7m9FVc+F25XtaO7T7by1XQLZ99mnro2LTHpX0OxOiM1gwyhYlkdJT9Us3l+JdVrPXQ7PJ1BU/JxZjfewLmzuI4toG76Arzz1uMYH72hy4T+PQhs2AyGgYgQqnMTqqrFv76Y+q9/oO6jWeQ8dnOnxiBGIuIYinKbP2ELGNVYQ+Zpw7OvsuBgSOX95LlP4qfMC5ibN5G+1ddQUDkNizJ30++miAiWrL8g9iEENpyDf/VorD3eNl0P0s3nTiL1++UMP/0O7Ju2UnXgIMqPHMWWMw8n7/XPSfv2V+oKerHyocsJORKoK+hJzjuzKZ80CpVgi8uJ0I4V5VgrPVirPFQe1bf5A5qhEzatw3z+soWAT/jjP/y4Gvn7lN0z/uawAduSteJZFSy4Zy2lP9fgzLKRXpBE3phUtsyrYt37pRz/8f7YkqL3I+WcNABsFupnLItqwmbNzyHpxIkUn3gltj7dsHbNIVhRQ7BsK5b0VHKfuhX78AFtPn9rbouGqv6DUiFEzHuzICj1WJUr1mFoEZneg5m4aSG/pt3I6pRH2OL8hFFl00n3taido2kZycdh6zMff+GJBNZNxNLlWSzpfzDVLdIVj16Ja0UREghSP6AbymYlbdYi0r79laoDBrHljImEHOE3voFkVzhJEyP+krWQIvu1JfS68QvqB2dhrfCQ/8h3LJ1xTrtOa97fclrcSUxV1FexLVkLhaC6PFxE98nLrMx/z+DQMzu/7ENncJf5WDBtLSl9nPxuzgGcvfRgJr81nAPu6MPkt0cQ9CnWvFMa1ZiMFAeO8b1xx6C8R/oNU0i/7nzsowpQ/gC27rmknH8iGX/9Y7uStdYQ5xgIVYFvRVSu11ZBcWPE8QjO3siqEhlR8QQHb/mMgNQwK28sy1PvJkQg1qG1i9gHY+v9HeKaYNoiu/UDu1M3pBfKFn5zm/Xxd/gzkik5bQIh1/ZC5d2eeR9fbvpOjeTjgfiD5D/yHX2u+ZR1D05i+TtnsOjni7HU+Mh5eWG7zh1fr4RmamNOCjHjaQv3n22lR4HCkQhlG2DTasGVAne856fbwI4fYisp+YbCwtfwesuw27Po0eM8cnImdOg1fnmiiIRkK+MeGrBtxG1HGQWJeMqj32LFeWwBFde/j39NObY+0Vu9ZDjsuCYeGLXrNRqDawxBIFQ/H4t9cExjaUpIfFiUvfkdtajL8Uzi8E1LWJxxBcvTbmeL8yNGlU0nKY7biDUU2Q1uvp7Q1kdR3qVYu//HVCNtDezFZaTPWcLSZ/5MMGn7m5q+t79EMNlF4VWnhjfEUSHP7OmL6frgt/z28olsPWngtttK/mwXttL2lWHSI2xah0lKgz+/GiAtF8o3Ciu+E0IhYdIfQlz8SIDeIzonWVu9+im83lJA4fWWsnr1U5SUfNOxFxIB2X57VCmFt8LP5vlVfHXRUjZ9W0nvk6NfusF1bGy6HgQrqtlyyVQgXCxX+QOoYJTnJiYMBCMV5Z4f3eu2kiKA6PfGppUQSmd02euMLv03tdYVzOyyH+uSnkMRh/M3IsJFdh/Bkv9CpHn8QSjvclONtAGE7Al4umUTTNq+eKvfzc+RsGkrm86bhC8rNbwxTpI156+l9L7mM9Y9OCmcrAGIkDxvA9atbqrHta/bif4tonWorgMUlzwSwOuGBAcE/FC0VFj0pYHdBcmZiv6jFVZbx1yvsPA1QiHvTttCIS+Fha916ChbvzNy+eL8Umb+cSkZQ5MQC9QWealaWU9CqpVj3h5BSq/o3/ay9cvCOiCb+hnLSLn8kKhd15KeQsKQvoS8Pgx7QrgdDeFEVjrgl2tL5rGJGIjzIFS9uVeSKUKg9Htjs+tWfyaZ3nH8lDmFhZmXsNn5IfuXv4A9FP06ix3Fkn4RkjCQQNHv8K8Zg7Xbv0010ubPTKHqgEEM/f00yo86gNTvlhJMcrL+mtOp2b/ftpIg8SJpwSaqD+1B6XnDto0KOn7bSsa7y/HlJ+Pt3r5SMjph0zqF3Qlfvmqw8AuD+mowLFCxWdi8Vjjk9BBTpgVwJLb/Ol5v41Wn97S9rdIHJ3LYs4NZ/FgR5Ytq8FUFcOYl0P+cPPInpOHKjd0tL9dxg6l+ci6hWi9GUvTiSL/qXABCtfV4fl6GJTMNe8HOK6FUKIQYbful26KkzTWWUOndqGANYjHpSkxRustBnHAGu3FwyWesTn6Mpek38VX+cEaWvUyu55hYh9ZmRuIh2Pr8QKDoJAKFx2HJfRD3i9ciIqZI3AqvOwN3v64YHh+e7jlsOvdIsO4+7SQeSCCIskZ+1kVI/Hkzmf9bRvL3xRTdNh5fj9Sd9/e37q6ETti0DufzwKN/tFK0TBg1OcSgMYoufRXdBin8HvjLBBuz3zSYNKX9CxDs9qzI7dDdt3e07JEpHPHPIfiqA1gTLaAUlSvqKfm+GnuGDUeGjfTBHZCFtpLz2AKqH56F+4uVJJ48LOrXr31vJlvvfYHks4+h4qFXSTzqYBxjR2DJSMVI7NxRR8M1lhChcAHdpNYX6o0KJeFRNi0uCAb9aq4h23MEC7LOZV7usfSuvoKhlQ/EbfkPSeiJtfdcAhsvILjlzyjvEixdnjHNaFvpieN23hBHc9Z2VDWxNz3/OpMet83EqPNjX1+FKMWGm8ZRdfguda5CiuRvN7Tq/Dph0zrc0rlCZYlw9QsB+u6/Q2NwBXYXDBqjWPl9xyRsPXqcx+rVT+10W9Qw7PTocV67z70nCSlWlr1czMaZW/FXh98hVa9z493qZ8il3Rh1c3RbrDgO7oWkOnDPWBaThM0+fADWXvmkX/N7PN8txrd8HaV/fhDnoaMxkhNJPmty+LZpJ9je8WAemDRhEywg8VV7UINU/zAmbPqepek3szrlEcocXzG67A1S/cNjHVqbiJGItdt/CZbeRah0Ksq7clu9NjMkbTuJw2QNwNs7jV++Pp8uT/6AtbSesjMKcA/Jpn5o5Lb6jomoIdTtn9eq80c1YRORDOBF4CigDLhZKfWvRvabEtnPvcPm45VSX0chTK2d1iw0sCZA3/3VTt+fIrDyB6FwqXDWrR2zfL5hnlpTq0Q7chWprzrAV1N+pX6Lj64T08kZnUJybyep/Vx4yny8c+iPdDs8g9yDUps/WQcRmwXnUQOp/3hZu25BtpVtQE+Ux4fyeHEdfhD2kYNxHjaa8tuewLdiHbbuebgO75wVpWJJQ+xDCNV/i1lvooiyotAJWzyy4GBYxcPkuCfzU+YUvulyIEMq7qdPzVUI8ZdUiBhYc+4iZB9KYOMF+NccgLX7++ZM2hrhWl5I/qufsua28wk5zbny2j0oizWPTgZh58QzpMDY/rXh9hNMad1ziPYI25OAD8gF9gM+EpFFSqlfG9l3nlIqerOotQ5z4PEh3n3Ewrx3DfafFGLNQmHZtwYLvzJYMV847NwQQw7puBVYOTkT9piANawibRiBa1hF2nBcaxV9Vo6/Lshhzw4mY2jSTo/ZEp1k759C8TcVUU3YILxatP7NRfgWbMB+QI+oXhulsGSkUnbLYwQravCvWo8KhnCMHEzaVeeQMLRfm0/dsnlsBxOqetO0BXQNEgiKt/kdNdPK9RzN4ZsW83PmRSzJuIYS56fsX/YyjlDntmDrLEbq6VgT+hEoPJHA2nFYu70aF0lb0pI1ZL//Lc41m1j++FX4s9NiHVLjIolZziuLsK+vouj2Q3dK1gAy31xK6qzC1p22wwJshogkAqcCtymlapVSc4D3gd9HKwYtOroNVFxwT4D3HrVwXn4CT11u5bcFwpBxIe7/xs9lTwQ6bJVoc5paRdoWRZ9vJb0gkYyhSbv1Di2eXYG/Pkj+hOg3+nZOHgSGUP9RdMt71L77FYWjz8K/pgjPT8tIPvVI8l67j14L3yLvpbtJu/h0rDkZnRqDOMdCqBK8yzv1Om1lKDsh8cQ6DK2d7KFsDip9j+HlT1Bqn8nM/BFscXwa67DazHDuj63PD4hjOIGi0wiWTMX94vmxDqtJJacfxvLHrsS1agPDz74b18qiWIfUpKrDeuHtGX7zLt7ATq1+ys4YQuoXa1p1vmi+HR0ABJVSK3fYtggYsof99xeRMhFZKSK3iUijo4EicrGI/CgiP5aVVXd0zFobHXF+iBte8/Pcch+3vevnD/cFOPnaIL2Hh2+TRqtFVUevIu15XBaFn5az6dtKRIQtP1Sx6NFCPjjmZ2Ycv5CsEUlRH10DsGQmYh/bK+pdD5wTRtP102fIe3UaznH7k3zG0dgH79wmq7EG8R3JcIUnLIfc33bqddrKopwExd38jprpCUKf2ss5bPMP2IPZzMudzJL0PxMkPkdQxZaHtddMjNTzCZbeQXDDWbhfON109dp2VHH4SH559a9IIMjQ8+4hbfbiWIe0R96eqZRcMALxBMh79iccK7cC4eRNOaysfXRyq84XzYQtCajaZVsV0Nha/FnAUCCH8Kjc2cANjZ1UKfWcUmq0Ump0Vlb7apxoHSuzK2R0gdxe4Y+GMh4i0ZtTuqfVom1dRdrzuCwKLurKnCtX8ELaTL65ZDmb51SSd1AKp8w5gIMfjE5bpsa4jh2Mb+FGAhsqo3ZNS3oKtq65JAzuQ9a0q1GhEIHiUryLV1L35Xxq3/2KUGVNu65x4YXvNb1DQn+wZKHq57brOp3FolwEpX0VzjVzSfEPZcLm7+ldcxmrUx5iVt7B1Fp/i3VYbSKGA0vXf2LJfYBQ9ZsE1o5H+TeYOmmrK+jF4n/fjqd7DoMvf4Tcf38V65CalTKnkC7P/AiAskfGn0KtG7mI5hy2WmDXjCoF2O23uVJqx3HCJSIylXDCdm/nhaftjTp6FalhEfb7c096nZCNWCDkVxhWwZmbQEKyddtt0o4oHttazmMHU3HLDNwfLyP5/8ZG7boqFAIRvItXUvPGDHzL1xKqrkMSrFhyMqj7fB5JvzuCxCPGdMr1RSQ8j82kCZs1lETQqIt1GFoHsygnI7Y+SbZ7Ej9nXsTMLvszYuvT9KiLv1k+IoIl6wbEPpjAhnMiixHeNfW8Nl9eBr+8+lcG3PA0fe9+Fee6zay74SxTFttVDiurnzyGEWNfQlkNyk8aSMKmWnr95YtWnSeaCdtKwCoi/ZVSDW9FRgCNLTjYlYI4XJKjAe1fpblkye1UV28f9k5JGc6wYVNbdP6cnAlUVy9jy5bPgBBgkJ09sVXX3/X83bufS+6AwxrdNxaJWgNbQS7WXunUfxS9hE0phRgGdV/Mp+LBl7GPKiDzjktxjCpAEmwEq2upfetzKp94o9MSNgjfFg3WvI8KlCBWc1Wmt6pkAtK+UUbNvPLdJ5O+aTQ/Zp3LT1nnU+r4nOFbn8SmTFrIuQlG8vFYe88jUHgCgXUTsOS/aOqkLZToYPnjV9PrgTfIn/4ZjsItrHzwUkKJjuYPjrJAdiKLvruI/n94n563zMRa7qbsrKHwj59afI6opaJKqTrgbWCqiCSKyDjgJGD6rvuKyDEikhv5fBBwG9DMfRHNjNrb63PXZA2gunoxS5bc3qLzl5R8Q2npTNhWuDREaenMFl+/sfOvWfN0x/cq7QAigvO4Ajxf/Uao3he1awZKt1I9/QNSLjyF7GlX4xw7AkkIryqxpCSRfMbRBMsqO3Uum7jCC8rNeFvUGkrBb+w6G0TbmziD3Thky1cMqryTosTX+brLKCptP8c6rDYxHEOw9fkecY4huPE8Alv+ivtFE48aWgzW3Xwua245j/TZixl6/jQSNm+NdVSNCmS6WP7W6Sz/3+ks++As1t97eKuOj/bY4WWAEygB3gAuVUr9KiI9RKRWRBrqERwBLBaROmAG4URvWpRj1TpAe1dp7pqs7bq9ufO39/odvcq0s7mOHYzyBPDMXBW1a1oyUvEtW0PyaZN22h7y+vCtWEfJdQ+SOGksBNpei6y5eWziGAViN+VtUVsoDb9RGeswtE4mWBhUdQeHbJlJUOqZ1WUMxc63Yx1Wm4g1C2vPzzDSLyZUdi+Bot+hvOZe6bz5nCNZ9tS1OAtLGHb2VBKXrY91SI1SCRYCWS68vVq/OC2qCZtSaqtS6mSlVKJSqkdD0VylVKFSKkkpVRj5+nqlVG5kvz5KqduVUv5oxqp1jM7u9dnc+dt7/Wj1Ku0ojkP7Ikl26j9aGrVrisVCQr8eVDw8nbpPv8U992fqPvuW6lfeo/K5NzGSXaRccOK2Ube2aippE8OOOEej6ue06xqdQSds+5Ys76FM3LSQ/LozSPd1TsHoaBAjAUuXZ7DkPYqq+YDau54itHX3NoBmUjl+OEteuwUMg6G/n0b6TBOPcrZh+oz5Zudpe5WOXqXZ2vO39/otPX7XmmyxInYrziP74/54eVRjypp2FcHySqpefJvq1z+ievoHeBetxD58IBnXT8HWM7/TYxDXISjPT6iQuVZkJoQyCBg1hNDvOfcV9lAWo8un4wx2i3Uo7SIiWDKvwtrzY5R/PbX3PUD9E20vhB0N9QO7s/jft+Puk8+gKx+jy6ufRq+OVCfTCZvWqXr0OA/D2Ln9RmtWaaakNN63r2F7c+dv7/Vbcvyc61bw2RlLWnS+aHAeV0BwYxW+hcVRu6atV1ey772G3OduJ/2qc8l58hZyn7yF5NMmIZ3UR3RXhms8KD/K/X1UrtdSCaFw4WCfYc55NZo5BPGyJP06FmVcxvdZZ+AxNsc6pG2MpKOw9fkOLGkE1h1O3UOxjqhp/uw0fnnlJrYeMZLe979Bn7unt2tKhlnohE3rVDk5E0hKGhj+IlIwN+QfuNMqzSVLbmfu3JO3fTQsKAAYNmwqDkf3nc7pcHTftko0J2cCffteht2eDQh2ezZ9+1620yrR7OyJbP9Wb90q0ebOD2CxGayfUYavumP6o7aX65jBIII7irdFG1jSUjDSkqn7eA5ltz5O2S2PUXbLY2w84Qpq3vmSkKfzCoyK62BAUHWzO+0abZEQzAbAZzHnbXQt9mqtq5iZP4LKhB9x+ftiD2UzM38/3JaNsQ5tG7EPxNZ7PuI6hODGKdRO+7XTi2K3R8hpZ8XDl7PxD8eQ95+vGHz5I1hq47uAdbR7iWr7mFWrntm+cEDCtVmUsZhVq56hX78/NbkKdNiwqZSUfIPPV7LT4z5fCSUl3+yUlDXVS7SxVaIpKYNblbQ1tW+vE7JY9HAhhZ+U0++M2PcWtOQkYT+wO/UfLSXt1knNH9CB3PMXU/3yu2CzYuvdlYRBvTFSkwhV1VL3/teEtlaRetHv2nz+pnqLiiUdsQ8lVD/bVI3g7aFwwuY1zD3/R4sNt2UDP2f+kcRAH8aWzNi2vd5SSI1tGc5g1xhGtzOxZmDt+QnBTVcTKn+Q2ruOJ+nm4xCHM9ahNc4wWH/9mbh75tL37lcZet49LH/qGrz5HTMlJ9r0CJvWqcL1z3Ymsn17e1eBNicaqzxzx6bhyLKx7gPz/EF2HluAb8EGApui164tWFFN1fNvYcnNJOPGC0m/+jxSzjuepBMOC/970kTqv/yuU2MQ1yEo9zyUMsdoJ4A9GE7ivZYtMY5EM6Ml6dcRlPqdkrU662qqEhYgJiw/KmLDmv8Uli5Pomo/pnbqk6ZfjFBy+mEsffbP2DeXM+ysqSQtaV0PT7PQCZvWyfY0ZN6yofR4WOVpWCTcY/STcoJ+c9wicB03GAD3x9HrLepbtoZgWSVZUy/H1j0Pse48zuVftxFrt84dgZTE8RCqRXkWdep1WmN7wmaeOUmaOWxyvkeJ8zPGlLy/bVtQ3GxxfkyG92AS/ead4G/JuAxrz09Q/g3U3nc/gTUrmz8ohqrGDmHJa7cSciQwZMp9ZHz+Y6xDajWdsGmdrPFvMRVq2bdetFZ5tlev47PxVQXYNKuyQ8/bVrZhXbD0SKP+w+jNY0so6EtgUym+VYXbtgXLK6n7fB4lV91L7UezSL34tE6NwXAdCoCqm9Wp12mNhFAGoqx4dMKm7cJnVJDtPgJHKA8ARZBSx1dscXxMin84rmDPGEfYNCPpyMhihAzqn3qQun+YezWmu19XlrxxO/UDuzPw2ifJf2lGXK0g1Qmb1qlyc4/abZtSsHLWZKD9q0Cb097jW6rbpAysTsM0t0VFBFdD1wN3dMpJWNKSST7jaMr/9izFZ91A8anXsuWKaVS//iFGWgo5j91MQr8e7S430mQ9NltXsPUmVG+ehQeCgSPYBY8leqt2tfggCF7Lpm1fFyW+zvrEl7CHchlYdRsAIcxze78xYh+Arc98xDWBYPEfqJ32i6kXI/gzU/j1pRspn3wAvf7xX/rc+U/Eb+7XuIFedKC1u9fnqlXP7NSrMzf3KPr1+xMA/fr9iZKS2YQ7k4WpQCLv3nUlR5/uY9iwqcyde/Ju59xxFehvvz2202OhUGCn+L777kICge0lE6zWDA466KVtx3d0L9HGXh+by0K3IzJY92EZ4x4eENOeog2cxw6m5ulv8Xy9KrxyNAoyrp+C+9uF+H4rxJKWjJHswpKXha1PNwxHOHHu7NfGSDyUUM1H4T6nJvh/ACIJ26bmd9T2Kd3rzmdd0rN8nXcgoLAoJxnesQyougVBCOHDIFwWp96yni3OGbitRSgU/aqvxR4yR99csaRj7TmD4KZrCJX/ndqpJ5B007GmXYwQciSw8oE/4e6eS/fnPsCxsYwVD11GMCUx1qE1SY+w7ePa2+sznKx9wo6rMLds+YRVq54BYMGCK3dK1gAMWx1TXriE+e8ZzJ17aqPnbdg+d+4ZwK71c4KR7bsnawCBwFa+++7Cbc+vo3uJ7un16XViNrWFHsoX1rbo3J3NeVg/JDEh6uU9nAfvR+oFJ5J00kRchx+EvaDvtmQtGsR1KATLwBu9+XvNcQS64bFsiHUYmskIwqFbvqVf9XX0rbmG0WVvMKjyLmwqhRD+bclaUeLrLEu7jcKkf2INpeKxFPNF/iAqbQtj+wR2EF6M8CSWvCdQNTPMvxjBMCi6+lR++9tFpPywnGHn3oN9g4njRSds+7z2rqJsbBXojts9nqJGH8/pU8h3Hxjsnow1aNi+pybm4e27JmsNGrZHc5Vpz2OzQGCtWW6L2q04jxxA/UfLot6JobOv19Rt0YZ5bKF688xjcwa74bbqhE1rXLf6s+hedy7OYFe8lnAZI4NwK7fNzg9ZnnoXPksZ+XVnMKD6RkaVv8LAqttYmToNn1ERy9B3Y8m8PNIZoYja+x4gsPa3WIfUpNJTxrP0+etJKKtk+NlTSVoUvT7MraUTtn1c+1dRtn0V6PL5nf/tF81Vps6cBPLGpppmHhuA8/jodz2Azr/t2aSEvmDNR9W1bBQ1GpzBbgSMGvwSvTIrWvypSPiBr7uMxGeUA1BrXcna5KcISi2J/v5sdcxldu54QgToV3Mt/atvICGUDoDCPJPnjaRJkcUIqdQ/+SC+H+fGOqQmVR84mMX/uo1gooMhf7ifzE/N1S2lgU7Y9nHtX0W5p2+hpr+1Gv6ed/bAT7RXmfY6IZvyRbXUrDdHRe1Ydj2IFRHBcB1KqH6WaXq8OgM9AHBbC5vZU9uXpfsOYOKmxSSEMgFwWzfgNUoYWf5Phlc8ykGlb2MoO5udH27bHyCEn4DUxCzuxoQ7I3yHuA7B88bz1N67zNSLETy9u7D4X7dRV9CLgdc9RdfnPzTdClKdsO3j2ruKsrFVoDtu37WtVAOHozt5fRXBwJ5q0jds31MfyvB2qzWj0Ucbtkd7lWmvE8NV7dd9aI42RDt2PdiXSOKhECgG3+pYhwKAK5Kw1Vt0wqY1zRnM3/Z5qeNLbKE0cjxHEWT71Ix669ptn69Kfojvs09nfs6J/JR5YVRjbU5DZwQj/RJCZfdTO/U9lNcT67D2KJCRwq8v3kDpcWPo+chb9L3tJcRnnhWkOmHbx7WkV2ZT+vX7E7m5k9mxV2du7uRtq0RHjXq80V6go0Y9zpgTgzx6/AewWyMhC+PG/Q+AceP+y+5JW0JkOxx00Eu7JW27rhJtz/Nr7fFp/V2kD3KZ67ZoQ9eD4qqoX9u7eCVltzyG8nV8aZGm57GF/39C9ea4LeqM1NOqt66LbSBaXEnyD0Aic9kshEfWKhN+IscTfkP8S9r1LEu7lRz3JAZV3kmtdQU/Zf4hliHvRsSGpcvTWPIeRdV8QO3UpwlVlMc6rD1S9gR+u/8Sii49idx3ZlNwyT+wVNU1f2AUiFluGXSEUaP6qfnz/xHrMPY67S37sSdL5wo3TUzghg8ew0j6lMbKgkDTZUPM6LtbVrHo4UIu2Dgee7ot1uHgW7KJ4lEPkfn0aSRfdFBUr1335XxKr7qP3JfvxnngsE65RmO9RZVS+FfkYiRNxtrt1U65bmsoQnzQw0mf6qsZWvlArMPR4sjs3PGExE+SfyDFrrcYUnk/fWquYEXKNNYmP8FBpe9tuzVakfAjy9Ju5cDSt7EqV4wj312o5hMCG84Ew4nrsoux9uwb65CalP3+XPre/jKe7tkse+pavN07vozKlIQpC5RSo1uyrx5h05rU3rIfTRk4RnHsjU8giR+zp7IgzZUNMaNeJ2YTCijWf2yOd5G2oXlYeqbH5Laoc8wIsFpxz/4pqtcVESTxUNOsFBUMnIGeO93K0rSWGL9lNr1qLibHfTQHlb5Dn5orKLfPYUXq3YzY+uy2ZA1gk+ttFEFTJmsARvJkbL3ngSRS//gD+H+aH+uQmlR64jiWvnADtvJqhp99N8k/x3bFq07YtCZ1ZvN0iwWGHvUxjS0obCgL0lzZEDPKOSAFV16CaW6LigiuYwfj+TJ6XQ8aGIlOHCMH454T3YQNwHAdBv71KJ85kqTEQB+dsGlt0rPuQrrXn7NtLtuvaTfSp+ZKurhP2LZPRcL31FnXkus+Ztu2IB4CUh+LkPdIHAXY+nyHOA/C/fozeD5529SLEapHD2TJG7cRSHYx5ML7yZwRuyRTJ2xakzq7ebpIc2VB2tc8PhbECDeDL/qsnKDXHHG6ji9Auf14vor+O0Tn+JH4V64nsDm6CzEkMTKPzSTlPRIDfaizrol1GFqcM7CREMok0zt+27Zq21I2JP4bv1FJ97rf47ZsZHXyo8zKG8f8nONYnfxYE2eMPrFmYe35OUbahfg+f5+6uz9G+bzNHxgjnp55LHnjNmqG9WHgDc/Q7Zn3Y7KCVCdsWpM6vXm6NFcWpG1lQ2Kt1wnZ+GuCbPzaHEUtHYf2RZLssbktOn4kAO45P3fK+fe0+EDsQ8CShar/ulOu21ouf1/8lgp8RuPFnjWtOQpFUDwEpZ7qhEUAlDi+YF3SM1TZFjGk4gH8RgVL026h2PU2PeqmMKDqFlak/o11SS/GOPqdiZGAJf8FLLkPEKp+i9q7nidUZY7fl40JpCWx9IUbKDlhLD0ef5t+t7wQ9RWk5v6rp8VcZzdPz809qtE3Kg1lQZorG2JWXQ9Px5poMc9tUbsV56QBuGdEv+uBrV8PLHmZuGcviOp1RQwkcQKhuq+jet09SQr0A6DOao5SI1r8EQSrcjG04iFWJT/MtzlH8332aSgUQyrvxRHMY3nqVAxlpaDyXvrWXEmO50h611y6U5N5sxARLFk3YO3+Lsq3jNppfye4YV2sw9ojlWBj1b0XU3j5KeS8N5eCi/+OtTJ6rQijmrCJSIaIvCMidSKyXkTOaWLfa0Vks4hUichLIhK9ZoTaNu0ti9Gcfv3+hKo5hlCg8bIgzZUNMSurw0KPozJY90EpKmSOldiu4woIFlfj+3ljVK8rIjgPGYl73qJOKe/RlO3z2NZF9bqNSYwkbLVWc7fq0cwv1T+cSRtXM6jyTsZvnsXwikdI9x3IuqTnCYmXbnXnkek9eNv+1QmLqTPx/Ekj5USsvb8FsVD3yP34F/8Y65D2TIQNl53EyvsvJnnhKoad+zcc67dE5dLRHmF7knATyFzgXOBpERmy604icjRwE3AE0AvoA9wVvTC1HeXkTGD06OcZN+4dRo9+vsOStQb7j72Eh475kN8+/IBx497eLRnr1+9PjBv3NuPGvdvo42bV64Rs6jf5KFlgjnZEzmMGgSHUf/Br9K89fhSqzo1n4fJOOf8eb4smHgZAqG5mp1y3NRL9fUEJdTadsGntl6DSyPCNJdU/HMGCIsgm19tkeg8l23vYtv2KXP9iq30e/aqvBczVwmpHhmM4tj7fI47huF95Au+XH5qmU0ljyo4/mF9fvAFrZS3Dzrmb5J86/+c6agmbiCQCpwK3KaVqlVJzgPeB3zey+wXAi0qpX5VSFcDdwJRoxapFV1IajJocwmfeAtht0uPYLJJ6OKjftKcG9tFlyU7CcUR/lCf6lbudY4Zj7ZpDqCK6yavYhyD2oaBi3yrMgoNM7yFYlDPWoWh7oaqERfiMrfSq/eO2bWX2WaxJeZx+1deR5B8AhG+rmpVYc7H2+hoj9Wy8n3yOMvGcNoCaUQNZ8q9bCaQm0u2ZPRfy7ihRK5wrIvsD3yq1/beViFwPTFBKnbDLvouAaUqp/0S+zgJKgSylVPku+14MXBz5cijwS+c9i71eFmCOnkrxSb9+badfu/bRr1/76Nev7fRr1z4DlVLJLdnR2tmR7CAJ2LU3ThXQWKC77tvweTKwU8KmlHoOeA5ARH5sacVgbXf69Wsf/fq1nX7t2ke/fu2jX7+2069d+4hIiyfsRXMOWy2Qssu2FKCmBfs2fN7YvpqmaZqmaXu1aCZsKwGriPTfYdsIoLEZ0L9GHttxvy273g7VNE3TNE3bF0QtYVNK1QFvA1NFJFFExgEnAdMb2f1V4CIRKRCRdOBW4J8tuMxzHRXvPkq/fu2jX7+2069d++jXr33069d2+rVrnxa/flFbdADhOmzAS8AkwnPRblJK/UtEegBLgQKlVGFk3+uAGwEn8D/gT0op8/au0DRN0zRN6yRRTdg0TdM0TdO01tOtqTRN0zRN00xOJ2yapmmapmkmt1ckbK3pUartTESuEJEfRcQrIv+MdTzxRkTsIvJi5PuuRkR+FpFjYh1XvBCR10Rkk4hUi8hKEflj80dpuxKR/iLiEZHXYh1LPBGRryOvW23kY0WsY4o3InKWiCyL/P1dLSLjYx2T2e3w/dbwERSRx5s7LpqFczvTjj1K9wM+EpFFSqnoN02MP8XA34CjCS/w0FrHChQBE4BC4FjgvyIyTCm1LpaBxYl7gYuUUl4RGQR8LSI/K6UWxDqwOPMk8EOsg4hTVyilXoh1EPFIRCYB9wNnAt8DXWIbUXxQSiU1fB5p27kFeLO54+J+hK2VPUq1XSil3lZKvcsuHSS0llFK1Sml7lRKrVNKhZRSHwJrgVGxji0eRPoFN6z+VpGPvjEMKe6IyFlAJfBljEPR9j13AVOVUvMjv/82KqU2xjqoOHMaUALMbm7HuE/YgAFAUCm1codti4AhMYpH24eJSC7h70k9uttCIvKUiNQDy4FNwIwYhxQ3RCQFmAr8OdaxxLF7RaRMROaKyGGxDiZeiIgFGA1ki8gqEdkgIk+IiL5T0zoXAK+qFpTs2BsSttb0KNW0TiMiNuB14BWl1PJYxxMvlFKXEf55HU+4uLaut9hydwMvKqWKYh1InLoR6AN0JVzA9AMR0SO8LZML2AiPEI0nPB1pf8KF7rUWiNSgnQC80pL994aErTU9SjWtU4iIQbhrhw+4IsbhxB2lVDAynaEbcGms44kHIrIfcCTwcIxDiVtKqe+UUjVKKa9S6hVgLuF5qFrz3JF/H1dKbVJKlQEPoV+/1jgfmKOUWtuSnfeGRQfbepQqpX6LbNtTj1JN63AiIsCLhN9xHquU8sc4pHhmRc9ha6nDgF5AYfhbkCTAIiIFSqmRMYwrnilAYh1EPFBKVYjIBsKvmdY25wP3tXTnuB9ha2WPUm0XImIVEQdgIfzL3iEie0MiH01PA4OBE5RS7uZ21sJEJCdSEiBJRCwicjRwNvBVrGOLE88RTm73i3w8A3xEeMW31gwRSRORoxt+54nIucChwKexji2OvAxcGflZTgeuAT6MbUjxQUQOJnwrvtnVoQ32lj/MlxHuUVpCeLXjpbqkR4vdCtyxw9fnEV75c2dMookzItITuITwvKvNkZEOgEuUUq/HLLD4oAjf/nyG8JvH9cA1Sqn3YhpVnFBK1QP1DV+LSC3gUUqVxi6quGIjXNJoEBAkvOjlZKWUrsXWcncDWYTvdHmA/wL3xDSi+HEB8LZSqsXTt3QvUU3TNE3TNJOL+1uimqZpmqZpezudsGmapmmappmcTtg0TdM0TdNMTidsmqZpmqZpJqcTNk3TNE3TNJPTCZumaZqmaZrJ6YRN07R9loisE5Hrm3h8SqS+mSmIyD9FRBcm1bR9kE7YNE2LqUgSoiIffhFZIyJ/F5HEFh7fK3Ls6M6ONVr2xuekaVr77C2dDjRNi29fAL8nXH1+PPACkIhuBK9pmgboETZN08zBq5TarJQqUkr9C3gdOBlAwv4iIqtFxC0iS0TkvB2OXRv594fIqNTXkeMOEJHPRKRMRKpFZI6IjG1voCJygogsEBGPiKwVkXtEJGGHx9eJyK0i8mzkuhtE5IZdzjFARL6JnGOFiBwrIrUiMqWp57TD8VeLyEYRqRCRl0XE1d7npWmauemETdM0M3ITHm2DcL/Hi4DLgQLgXuBZETku8viBkX8nA12A30W+TgamEx6xOxBYCMwQkay2BhVpUP868AQwBLgQOA2Ytsuu1wJLgJHA/cADDcmiiBjAO0AAGANMIdzP177D8Xt6TkSez1DgSOBM4BTg6rY+J03T4oO+JappmqmIyIHAOcCXkXls1wFHKaVmR3ZZG9nncuAjoKHZeblSanPDeZRSX+1y3iuBUwknQa+1MbxbgAeVUi9Hvl4tIjcCr4nIDWp7c+bPlFJPRD5/XESuAo4A5gGTgIGR57QxEtu1wNwdrtPoc4qoBi5VSgWAZSLyZuTc97bxOWmaFgd0wqZpmhlMjqzGtBIeWXsPuJLwiJoD+ERE1A7724B1TZ1QRHKAu4GJQC5gAZxAj3bEOQo4MJKkNTAi580DNkW2Ld7luGIgJ/L5IKC4IVmL+AEItTCGpZFkbcdzH9TCYzVNi1M6YdM0zQxmARcDfsLJjB9ARHpHHj8BKNzlGH8z53yFcKJ2LeHkzgt8CSQ0cUxzDOAu4M1GHivd4fNdY1Nsn4Iika/bqqlza5q2l9IJm6ZpZlCvlFrVyPalhBOtnrve4tyBL/KvZZfthwBXKaU+AhCRXMLzwdrjJ2DQHmJtqWVAVxHJV0oVR7aNZueka0/PSdO0fZRO2DRNMy2lVI2I/B34u4gI4ZG4JMKT9UNKqeeAEsKLFI4WkXWARylVBawEzhOR7wiXCHmA7YlQW00FPhSR9cB/CS8cGAocqJT6SwvP8TmwAnglUrTXCTwUOVfDyNuenpOmafsoPYyuaZrZ3QbcCVwP/Eo44TmVSOmLyHyuq4A/Ep7P9V7kuAsJJ3cLgH8DL9HMvLfmKKU+BY4jPC/u+8jHTex+u7apc4QIr+y0R45/BbiHcLLmaeY5aZq2j5Lti5o0TdO0WBCREYTLjoxWSi2IcTiappmQTtg0TdOiTEROAeqA34BehG+JCrC/0r+UNU1rhJ7DpmmaFn3JhAvqdgcqgK+Ba3WypmnanugRNk3TNE3TNJPTiw40TdM0TdNMTidsmqZpmqZpJqcTNk3TNE3TNJPTCZumaZqmaZrJ6YRN0zRN0zTN5P4fsDGHklnhOX4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0, x1 = np.meshgrid(\n",
    "        np.linspace(0, 8, 500).reshape(-1, 1),\n",
    "        np.linspace(0, 3.5, 200).reshape(-1, 1),\n",
    "    )\n",
    "X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "X_new_with_bias = np.c_[np.ones([len(X_new), 1]), X_new]\n",
    "\n",
    "logits = X_new_with_bias.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "zz1 = Y_proba[:, 1].reshape(x0.shape)\n",
    "zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "plt.figure(figsize=(10, 4))\n",
    "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris virginica\")\n",
    "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris versicolor\")\n",
    "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris setosa\")\n",
    "\n",
    "from matplotlib.colors import ListedColormap\n",
    "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "\n",
    "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n",
    "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n",
    "plt.clabel(contour, inline=1, fontsize=12)\n",
    "plt.xlabel(\"Petal length\", fontsize=14)\n",
    "plt.ylabel(\"Petal width\", fontsize=14)\n",
    "plt.legend(loc=\"upper left\", fontsize=14)\n",
    "plt.axis([0, 7, 0, 3.5])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now let's measure the final model's accuracy on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9333333333333333"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logits = X_test.dot(Theta)\n",
    "Y_proba = softmax(logits)\n",
    "y_predict = np.argmax(Y_proba, axis=1)\n",
    "\n",
    "accuracy_score = np.mean(y_predict == y_test)\n",
    "accuracy_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our perfect model turns out to have slight imperfections. This variability is likely due to the very small size of the dataset: depending on how you sample the training set, validation set and the test set, you can get quite different results. Try changing the random seed and running the code again a few times, you will see that the results will vary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.10"
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  "nav_menu": {},
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